WORKSHEET ON EVALUATING FUNCTIONS FOR SAT

Problem 1 :

If f(x) = 2x − 5, then what is the value of f(2) + f(5) ?

(A) 1    (B) 2    (C) 3    (D) 4      (E) 5

Solution

Problem 2 :

If h(x) = 3x + 5 and h(a) = 27, then what is the value of a ?

Solution

Problem 3 :

Let f(x) = 4x − 3. If f(a) = 9 and f(b) = 5, then what is f(a + b) ?

(A) 5      (B) 7     (C) 14        (D) 16       (E) 17

Solution

Problem 4 :

If f(x) = x² − 1, and f(2a) = 35, then what could be the value of a ?

(A) −6      (B) −3     (C) 1     (D) 2       (E) 6

Solution

Problem 5 :

If f(x) = 2x+ 4, then what is the value of f(4) + f(6) ?

(A) f(8)      (B) f(10)       (C) f(12)      (D) f(18)      (E) f(28)

Solution

Problem 6 :

z(q) = 4q + 1/2

The zoomster function z used in space flight engineering is defined above. If, for some number u, z(u + 1/2) = 1/2, then what is the value of u ?

(A) −3/2       (B) −1/2      (C) −1/8      (D) 1/8    (E) 1/2 

Solution

Problem 7 :

For the function f graphed in the xy plane above, if f(−2.5) = k, then what is f(2k) ?

Solution

Problem 8 :

The volume of a balloon is given by the equation

V = t² - 3t + 3

What is the volume of the balloon after 3 seconds ?

(A) 3       (B) 6      (C) 9      (D) 12

Solution

Problem 9 :

In the table above, if y = x² + x - 2, what is the value of k ?

Solution

Problem 10 :

The distance d, in meters, traveled by a rocket depends on the amount of fuel f, in liters, it burns according to the equation d = (2/3)f . Based on the table above, how many rockets traveled more than 20 meters ?

(A) one       (B) Two      (C) Three      (D) Four

Solution

Problem 1 :

If f(x) = 3x - 1 and 2f(b) = 28, what is the value of f(2b) ?

Solution

Problem 2 :

The function f is defined by f(x) = (x - 7)² + 9. If f(a- 2) = 25, what is one possible value of a ?

Solution

Problem 3 :

A function f(x) has two properties :

f(a + b) = f(a) - b

f(2) = 10

What is the value of f(5) ?

a)  5     b)  7    c) 9      d)  11

Solution

Problem 4 :

If f(x + 1) = 3x + 2, the function f could be defined by which of the following?

a)  f(x) = 3x - 2      b)  f(x) = 3x - 1    c)  f(x) = 3x + 1

d)  f(x) = 3x + 5

Solution

Problem 5 :

The function f and g are defined by f(x) = x²+ 2 and g(x) = 4x- 3. If a > 0, for what value of a does g(f(a)) = 41 ?

Solution

Problem 6 :

The function f is defied by f(x) = (1/2)x + a, where a is a constant. If f(a) = 3, what is the value of f(8) ?

a)  6      b)  7       c)  8        d)  9

Solution

Problem 7 :

The table above displays several points on the graph of the function f in the xy-plane. Which of the following could be f(x) ?

a)  f(x) = 20x     b) f(x) = x + 20     c)  f(x) = x - 20

d) f(x) = x² + 20

Solution

Problem 8 :

For which of the following functions is it true that f(-3) = f(3) ?

a)  f(x) = 2/x     b)  f(x) = x²/3     c)  f(x) = 3x²+1   d)  f(x) = x+2

Solution

Problem 9 :

The function f is defined by f(x) = 3x + 2 and the function g is defined by g(x) = f(2x) - 1. What is the value of g(10) ?

Solution

Problem 10 :

If f(x) = (16 + x²)/2x for all x ≠ 0, what is the value of f(-4) ?

Solution

Problem 11 :

Several values of the function f are given in the table above. If f(x) = ax² + b, where a and b are constants, what is the value of f(3) ?

a)  23        b)  39       c)  43       d) 56

Solution

Problem 12 :

The table above gives some values for the function f. If g(x) = 2f(x), what is the value of k if g(k) = 8 ?

a)  2         b)  3            c)  4         d) 8

Solution