Graph Interpretation Word Problem: Temperature ~ In-depth Info

Algebra: Graphs, graphing equations and inequalitiesSection. You can put this solution on YOUR website! in functional notation. To draw the graph, plot the given vertex and the given point, and find some more points, saySince the graph of the function has a maximum at (-4,2). therefore, we can conclude that if the function is of a parabola then it must open down and the vertex of the parabola will be the maximum point i.e. (-4,2). So, option C matches the conditions which give 'On a coordinate plane, a parabola...Tempestt graphs a function that has a maximum located at (-4, 2). Which could be her graph? Which statements about the graph of the function f(x) = -x2 - 4x + 2 are true? Select three options. -The range is {y|y ≤ 6}. -The function is increasing over the interval (-∞ , -2). -The function has a...A complete graph is an undirected graph where each distinct pair of vertices has an unique edge connecting them. The correct answer is n*(n-1)/2. Each edge has been counted twice, hence the division by 2. A complete graph has the maximum number of edges, which is given by n choose 2...Сбор средств. 2 453 511 просмотров 2,4 млн просмотров. Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions.

Tempestt graphs a function that has a maximum located at...

Given are 4 graphs and we have to select the graph that has a maximum. at (-4,2). All the graphs seem to be that of a parabola. The curve has maximum only when it is open downward. Hence Option a and option b cannot be correct as these have a minimum and open upward.The graph of a function f is shown above. The graphs of the derivatives of the functions f, g, and h are shown above. Which of the functions f, g, or h have a relative maximum on the open interval a < x < b ?Where did this graph come from? We learn about sin and cos graphs later in Graphs of sin x and cos x. Note 3: We are talking about the domain and range of functions, which have at most one y-value for each x-value, not relations (which can have more than one.).Sketch the graph of a function on [-1,2] that has an absolute maximum but no local maximum. Given Problem. You can see that there are two locations where the slope of the tangent is zero, and there are local maxima.

Algebra 1: Quadratic Functions; standard form Flashcards | Quizlet

Please let me know if you have any questions. - mGalarnyk/datasciencecoursera. Consider the problem of predicting how well a student does in her second year of college/university, given how well she did in her first year.You can find more information about the Yahoo Answers shutdown and how to Working out the potential inside a uniform sphere of charge as a function of r, is pretty tricky. 1st find the field strength as a function of r. The sphere has radius R. The amount of charge...The location of each point on the graph depends on both the GPA and motivation scores. § Sam, for example, has a GPA of 2 so his point is located at 2 on the right. She is one of the students with the lowest GPA, but she has the maximum score on the...Problems on Functions adapted from questions set in previous Mathematics exams. (a) A function is represented by the following function machine. A number is input into the machine and the output is used as Work out what this number could have been. (c) Another function machine is shown below.Function geom_bar have default y value. By clicking "Accept all cookies", you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy.

1. GCSE Higher

$f(x) = \frac2x5 + 7$ and $g(x) = 10x^2 - 15$ for all values of $x$.

Find $fg(x)$.

Give your resolution in the form $ax^2 + b$ where $a$ and $b$ are integers.

Worked Solution

2. GCSE Higher

The function $f$ is described via the next components:

$$ f(x) = 3x^2 - 2x^3 $$

Calculate the value of $f(-5) $

Worked Solution

3. IGCSE Extended

The desk presentations some values (rounded to 1 decimal position) for the function $y=\frac2x^2-x, x\neq 0$.

$x$ -3 -2 -1 -0.5 0.5 1 2 3 4 $y$ 3.2 2.5 8.5 7.5 1.0 -2.8

(a) Complete the desk of values.

(b) Draw the graph of $y=\frac2x^2-x$ for $-3\le x \le -0.5$ and $0.5\le x\le 4$.

(d) Use your graph to resolve the equation $\frac2x^2-x=1-2x$

(e) By drawing a suitable tangent, to find an estimate of the gradient of the curve at the purpose where x = 1.

(f) Using algebra, display that you'll use the graph at $y=0$ to search out $\sqrt[3]2$

Worked Solution

4. GCSE Higher

(a) A function is represented by way of the following function system.

A bunch is enter into the gadget and the output is used as a new input.

If the second output is 53 work out the number that was once the primary input.

(b) A bunch is input into the gadget and the output produced is similar quantity. Work out what this number could were.

If the Input is two, the Output is 7. If the Input is 6, the Output is 27. Use this knowledge to fill in the two containers.

Worked Solution

5. IGCSE Extended

If $f(x)=5-4x$ and $g(x)=4^-x$ then:

(a) Find $f(3x)$ in relation to $x$.

(b) Find $ff(x)$ in its most simple shape.

(d) Find $f^–1(x)$, the inverse of $f(x)$.

(e) Solve the equation $gf(x)= 1$.

Worked Solution

6. GCSE Higher

Here is a function system that produces two outputs, A and B.

Work out the variability of input values for which the output A is less than the output B.

Worked Solution

7. GCSE Higher

The functions $f$ and $g$ are such that:

$$ f(x) = 4x + 3 $$ $$ g(x) = x^2 - 3 $$

(a) Find $f^-1(x)$

(b) Given that $gf(x) = 3fg(x)$, display that:

$$ 4x^2 + 24x + 33 = 0 $$

Worked Solution

8. IB Standard

Consider the graph of $f(x)=a\sin(b(x+c))+12$, for $0\le x\le 24$.

The graph has a maximum at (8, 22) and a minimal at (18, 2).

(a) Find the worth of $a$.

(b) Find the value of $b$.

(d) Solve $f(x)=5$.

Worked Solution

9. IB Standard

Let $f (x)=a(x-b)^2+c$. The vertex of the graph of $f$ is at (4, -3) and the graph passes through (3, 2).

(a) Find the worth of $c$.

(b) Find the worth of $b$.

Worked Solution

10. IB Applications and Interpretation

The circumference of a given circle $C$ can be represented through the function $C(A) =2\sqrtA \pi, A \ge 0 $ where $A$ is the realm of the circle. The graph of the function $C$ is proven for $0 \le A \le 16$.

(a) Use the graph to search out the worth of $C(8)$ to the closest complete quantity.

(b) The range of $C(A)$ is $0 \le C(A) \le n$. Write down the value of $n$.

(d) In the context of the query, provide an explanation for the meaning of $ C^-1(12)$.

Worked Solution

11. IB Standard

The diagram shows the graph of $y=f(x)$, for $-3\le x \le 4$.

The graph passes in the course of the point (4,0.65).

(a) Find the value of $f(-2)$;

(b) Find the worth of $f^-1(0)$;

(d) Sketch the graph of $f^-1$.

Worked Solution

12. IB Applications and Interpretation

The circumference of a given circle $C$ can be represented by way of the function $C(A) = 2 \sqrtA \pi$ , $A \ge 0 $ , where $A$ is the world of the circle. The graph of the function $C$ is shown for $0 \le A \le 10$.

(a) Write down the worth of $C(5)$.

The vary of $C(A)$ is $0 \le C(A) \le k$.

(b) Find the worth of $okay$.

(d) In the context of the question, give an explanation for the meaning of $ C^-1(10) \approx 7.96$.

Worked Solution

13. IB Standard

The diagram shows part of the graph of $y=asinbx+c$ with a minimum at $(-2.5,-2)$ and a maximum at $(2.5,4)$.

(a) Find $a$.

(b) Find $b$.

Worked Solution

14. IB Standard

The Big Wheel at Fantasy Fun Fayre rotates clockwise at a constant pace completing 15 rotations each hour. The wheel has a diameter of 90 metres and the bottom of the wheel is 6 metres above the bottom.

A cabin starts at the bottom of the wheel with the highest of the cabin 6m above the bottom.

(a) Find the best height of the top of the cabin reaches as the wheel rotates.

After $t$ mins, the height $h(t)$ metres above the bottom of the top of a cabin is given by way of the function $h(t)=51-a\cos bt$.

(b) Find the period of $h(t)$

(d) Find the price of $a$.

(e) Sketch the graph of $h(t)$ , for $0\le t\le 5$.

(f) In one rotation of the wheel, find the chance that a randomly selected seat is at least 70 metres above the ground. Give your answer to two decimal puts.

Worked Solution

15. IB Standard

The population of sheep on a ranch is modelled by way of the function $P(t)= 65 \sin(0.4t-3.2)+450$, the place t is in months, and $t=1$ corresponds to 1st January 2015.

(a) Find the selection of sheep on the ranch on 1st July 2015.

(b) Find the velocity of change of the sheep population on 1st July 2015.

Worked Solution

16. IB Standard

Let $f(x)=5x^2-20x+ok$. The equation $f(x)=0$ has two equivalent roots.

(a) Write down the price of the discriminant.

(b) Hence, display that $k=20$.

The graph of $f$ has its vertex at the x-axis.

(d) Write down the answer of $f(x)=0$.

The function can be written within the form $f(x)=a(x-h)^2+j$.

(e) Find the price of $a$.

(f) Find the price of $h$.

(g) Find the worth of $j$.

(h) The graph of a function $g$ is got from the graph of $f$ by a mirrored image in the x-axis, followed by a translation via the vector $\beginpmatrix 0 \ 3 \ \endpmatrix $. Find $g$, giving your resolution in the form $g(x)=Ax^2+Bx+C$.

Worked Solution

17. IB Analysis and Approaches

The functions f and g are outlined as follows:

$$f(x) = \fracx+45$$ $$g(x) = 10x - 3$$

(a) Find $ (g \circ f)(x) $

(b) Given that $ (g \circ f)^-1 (a) = 5 $ , in finding the price of $a$.

Worked Solution

18. IB Standard

The diagram shows a part of the graph of $f(x)=Ae^kx+2$.

The y-intercept is at $(0,10)$.

(a) Show that $A=8$.

(b) Given that $f(8)=3.62$ (correct to a few significant figures), to find the worth of $okay$.

(ii) Hence, provide an explanation for why $f$ is a decreasing function.

(iii) Find the equation of the horizontal asymptote of the graph $f$.

Let $g(x)=-x^2+7x+5$

(d) Find the realm enclosed by the graphs of $f$ and $g$.

Worked Solution

19. IB Standard

Part of the graph of $f(x) = \log _b(x + 4)$ for $x > - 4$ is shown underneath.

The graph passes thru A(4, 3) , has an x-intercept at (-3, 0) and has an asymptote at $x = - 4$.

(a) Find the value of $b$.

The graph of $f(x)$ is reflected within the line $y = x$ to present the graph of $g(x)$.

(b) Write down the y-intercept of the graph of $g(x)$.

(d) Find $g(x)$ relating to $x$.

Worked Solution

20. A-Level

The purposes $f$ and $g$ are defined as:

$$ f(x) = \sqrt3x+4 \text for x \ge -1 $$ $$ g(x) = x^2 - 3x \textual content for all real values of x $$

(a) Find $ f^-1(x) $

(b) State the domain of $ f^-1$.

(d) Find $gf(x)$.

(e) Solve the equation $gf(x) = 10$.

Worked Solution

21. IB Standard

Let $f(x)=\sin ( \frac \pi4x) + \cos ( \frac \pi4x) $, for $-4\le x \le 4$

(a) Sketch the graph of $f$.

(b) Find the values of $x$ where the function is lowering.

(c) The function $f$ can also be written in the form $f(x)=a\sin ( \frac \pi4(x+c))$ the place $a\in \mathbf R$ and $0 \le c \le 2$. Find the value of $a$ and $c$.

Worked Solution

22. A-Level

The function $f$ is outlined as $f(x) = 12x^3 - 5x^2 -11x + 6 $.

(a) Use the Factor Theorem to show that $ (4x-3) $ is a issue of $f(x)$

(b) Express $f(x)$ as a product of linear factors.

(c) The function $g$ is defined as $ g( \theta )= 6 \cos \theta \cos 2\theta + 5 \sin^2 \theta - 5 \cos \theta + 1 $. Show that the function $ g( \theta ) $ can be written as $ f(x) $, the place $ x = \cos \theta $.

(d) Hence resolve the equation $ g(\theta ) = 0 $, giving your solutions, in radians, in the interval $0 \le \theta \le 2 \pi $.

Worked Solution

23. IB Analysis and Approaches

Consider a function $f$, such that $f(x)=7.2\sin(\frac\pi6x + 2) + b$ where $ 0\le x \le 12$

(a) Find the duration of $f$.

The function f has a native maximum at the purpose (11.18,10.3) , and a local minimum at (5.18.-4.1).

(b) Find the worth of b.

A 2d function $g$ is given by $g(x)=a\sin(\frac2\pi7(x -4)) + c$ the place $0 \le x \le 10$

The function $g$ passes throughout the issues (2.25,-3) and (5.75,7).

(d) Find the worth of $a$ and the value of $c$.

(e) Find the price of x for which the purposes have the best difference.

Worked Solution

24. A-Level

The height above the bottom, H metres, of a passenger on a Ferris wheel t mins after the wheel starts turning, is modelled through the next equation:

$$H = ok – 8\cos (60t)° + 5\sin (60t)°$$

where k is a constant.

(a) Express $H$ in the form $H = okay - R \cos(60t + a)° $ where $R$ and $a$ are constants to be found ($ 0° \lt a \lt 90° $).

(b) Given that the preliminary height of the passenger above the bottom is 2 metres, to find a complete equation for the style.

(d) Find the time taken for the passenger to reach the maximum height on the 5th cycle. (Solutions primarily based entirely on graphical or numerical methods are not acceptable.)

(e) It is made up our minds that, to extend earnings, the velocity of the wheel is to be greater. How would you adapt the equation of the fashion to replicate this build up in speed?

Worked Solution