EVALUATING FUNCTIONS PRACTICE PROBLEMS WORKSHEET FOR SAT

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