Functions ACTs

Suppose a quadratic function is given by the equation Q(x) = (x + 4)(x - 1). If R(x) is a reflection of Q(x) over the y-axis, through which two points must the graph of R(x) pass?

(-1,0) and (4,0)

The graph below shows two functions, f(x) and g(x). Which of the following statements is true?

(0,2) is a solution for f(x) = g(x)

Suppose the graph of g(x) passes through the points (5, -1). If g(x) is reflected over the line y = 3, through which point must the reflected graph pass?

(5,7)

Several values for the functions g(x) and h(x) are shown in the tables that follow. What is the value of g(h(3))?

-1

What is the fifth term in the geometric sequence -432, 72, -12, 2?

-1/3

The graph of g(x) = cos(3x) is shown below. Which of the following lists represents the values of x for which g(x) = 0?

-150°, -90°, -30°, 30°, 90°, 150°

If f(x) = 3^3x+3 and g(x) = 27^(2/3x-1/3), for what value of x, if any, does the graph of f(x) intersect the graph of g(x)?

-4

If the first four terms of an arithmetic sequence are 25, 21, 17, and 13, respectively, what is the 20th term of the sequence?

-51

A finite arithmetic sequence has five terms. The first term is 4. What is the difference between the mean and the median of the five terms?

0

The graph of the quadratic function f(x) = ax^2 + bx + c in the standard (x,y) coordinate plane is shown below. When f(x) = 0, which of the following best describes the solution set for x?

1 double real solution only

What value of x satisfies the equation log2 x = -3?

1/8

If logx 100 = 2, then x = ?

10

The first and seventh terms in a sequence are 1 and 365, respectively. If each term after the first in the sequence is formed by multiplying the preceding term by 3 and subtracting 1, what is the sixth term?

122

The two triangles in the figure below share a common side. What is sin (x + y)?

12sqr5 + sqr10/30

What value of x satisfies the equation log3 (5x - 40) - logs 5 = 2?

17

For what value of x is the equation log2 x + log2 (8x) = 5 true?

2

If log7 7^sqr7 = x, then x is between which of the following pairs of consecutive integers?

2 and 3

In the fifth and sixth terms of a geometric sequence are 3 and 1, respectively, what is the first term of the sequence?

243

If f(x) = 2(x + 7), then f(x + c) = ?

2x + 2c + 14

For the 2 functions f(x) and g(x), ordered pairs are shown below. What is the value of f(g(4)) f(x): {(4,1), (5,2), (6,3), (7,4)} g(x): {(-1,-4), (1,0), (2,2), (4,6)}

3

For the 2 functions f(x) and g(x), ordered pairs are shown below. What is the value of f(g(4))? f(x): {(4,1), (5,2), (6,3), (7,4)} g(x): {(-1,-4), (1,0), (2,2), (4,6)}

3

For the piecewise function f(x) defined below, what is the value of f(6)? f(x) = {x^2 + 5, is x < 0 {2x - 9, if 0 < x < 6 {4 + x, if x > 6

3

What is the smallest positive value for 0 where the graph of f(x) = sin 20 reaches its minimum value?

3pi/4

For how long, in hours and minutes, was Erin at or above 4,500 feet?

4 hours 20 minutes

If a function is defined by the rule r s = r(r - s) for all integers r and s, then 4 (3 5) equals which of the following?

40

In the geometric sequence 3, 12, r, 192, ... what is the value of r, the third term?

48

The lengths of the legs of the right triangle are below 5 sin x and 5 cos x respectively. If 0° < x < 90°, what is the length of the hypotenuse of the triangle?

5

What are the values of 0, between 0° and 360°, when sin 0 = sqr3/2?

60° and 120° only

The graph below shows Aaron's distance from home over a one-hour period, during which time he first went to the library to return some books, then went to the post office, and then returned home. Based on the graph, which of the following statements could be true?

Aaron spent 10 minutes at the library and 15 minutes at the post office

Which of the following correctly describes the range of the function h(x) = 4x^2 - 9?

All real numbers greater than or equal to -9

The figure shown here represents the function g(x) = sqrx. Suppose h(x) is a transformation of g(x) and is given by the equation h(x) = sqrx+1 + 3. Which of the following correctly states the domain and range of h(x)?

Domain: x > -1, Range: y > 3

Which graph best represents the absolute value of the velocity that Erin traveled, in vertical feet per hour.

Squares

Which of the following statements describes the total of the first n terms of the arithmetic sequence below? 1, 3, 5, 7, 9

The total is always equal to n^2

If the first and second terms of a geometric sequence are 6 and 18, what is the expression for the value of the 25th term of the sequence?

a25 = 3^24 x 6

The graph of the function f(x) = cos x in the standard (x,y) coordinate plane is reflected over the x-axis, shifted right pi units, and then shifted down a units. Which of the following functions represents the graph after the 3 transformations have been applied?

f'(x) = -cos(x - pi) - a

The following figures show regular polygons and the sum of the degrees of the angles in each polygon. Based on these figures, which equation represents the number of degrees in a regular polygon as a function of the number of sides, n, the polygon has?

f(n) = 180(n - 2)

Which function could have been used to generate the data given in the table below?

g(x) = (1/2)^x + 4

Which of the following piecewise function could have been used to generate the graph below?

g(x) = {-3/2x - 4, if x < 0 {sqrx - 1, if x > 0

The function f(x) = 0.5 sin(2x) is graphed below over the domain [0,2pi]. What is the period of the function?

pi

Which of the following is equivalent to tan0cos^20 + tan0sin^20/sin0?

sec 0

What is the value of the expression cos(5pi/12) given that 5pi/12 = 2pi/3 - pi/4 and that cos(x - y) = (cos x)(cos y) + (sin x)(sin y)?

sqr6 - sqr2/4

If x > 0, a = x cos 0, and b = x sin 0, then sqra^2+b^2 = ?

x

If a quadratic function is defined by q(x) = 2x^2 - x - 15, for what values of x does the graph of the function cross the x-axis?

x = -5/2, x = 3

If f(x) = 1/3x + 13 and g(x) = 3x^2 +6x + 12, which expression represents f(g(x))?

x^2 + 2x + 17

The entire graph of a function, F, is shown in the standard (x,y) coordinate plane below. One of the following sets is in the range of the function. Which set is it?

{0, 2, 4, 6}