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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Math 107 Exam 1 Practice

20. Use the graphs of f and g to evaluate the functions. Find: 21. Given the graph of f(x) on the axes below, find the following.

(a) Find the domain of f(x): ___________________________ interval notation

(b) Find the range of f(x): _____________________________ interval notation

(c) Over which interval(s) is the function increasing? ___________________________ interval notation

(d) Over which interval(s) is the function decreasing? ___________________________ interval notation

(e) Over which interval(s) is the function constant? _____________________________ interval notation  22. Using the function f(x) above (from #21), graph the function y = -f(x + 6) + 3 on the same axes; label the points of the transformed
graph. Describe the transformation verbally.

23. Let f(x) = x2 - 25 and . Find the following. 24. Find the mathematical model for the following: F varies jointly as r and the cube of s. When F = 4158, r = 11 and s = 3.
Use the math model to find r, when F = 6 and s = 2.

25. C varies inversely as t and directly as z. If C = 10, when t = 2 and z = 12, then use a math model to find C, when t = 3 and z = 6.

26. Identify and graph the parent function for .
Describe the transformation that occurs in the function, and then graph the function.
Identify any intercepts.

Describe : 27. Identify and graph the parent function for .

Describe the transformation that occurs in the function, and then graph the function.
Identify any intercepts.

Describe : 28. Given the quadratic function , find the following. BOX YOUR ANSWERS.

(a) vertex
(b) y-intercept
(c) x-intercept(s)
(d) Standard Form

29. Determine the Range of in interval notation.

30. Find the difference quotient: , where h ≠ 0, for each of the functions 31. A ball thrown into the air by a child follows a parabolic path. The ball reaches a maximum height of 20 feet when it is 6 feet away from
the child. If the ball is 5 feet off of the ground when the child releases the ball, then how far from the child will the ball be when it hits the
ground? (Hint: Let y = f(x) be the vertical distance (height) of the ball and x be the horizontal distance that the ball travels.)
Give an exact distance and an estimated distance (without using a calculator).

32. A machine producing toy trucks has a production time of 10 hours before it conks out each day. Its production of toy trucks follows a
model of T(x) = -120x2 + 1200x, where x is the production time in hours and T(x) is the number of toy trucks the machine produces.
At what time each day will the machine produce the maximum number of toy trucks if the company starts the machine at 7:00 am daily?

33. Given , find the following. Show your work when finding the vertex and the x-intercepts below.
Write NONE if that is the case. Sketch a graph of the function; label the vertex and the x- and y-intercepts on the graph.

 (a) Equation in Standard Form: _______________________________ (b) vertex: _____________ (c) axis of symmetry: _____________ (d) opens: up or down (e) vertical: stretch or shrink or average (with respect to its parent graph) (f) Domain: _______________ (g) Range: ______________ (h) y-intercept: ____________ (i) x-intercept(s): _____________________ 34. Write the quadratic function in Standard Form.

35. Given the graph of h(x), graph the following functions. Label the points that you graph clearly.
(8 points) 36. Identify and graph the parent function for .

Describe the transformation that occurs in the function, and then graph the function.
Identify any intercepts.

Describe : 37. - 40. (Examples 1-4 in Section 2.7)