PRACTICE PROBLEMS ON FUNCTION NOTATIONS FOR SAT

Problem 1 :

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

Solution

Problem 2 :

The function f is defined by f(x) = x²+bx+c where b and c are constants. If the graph of f has x-intercepts at -5 and 3, which of the following correctly gives the values of b and c ?

a)  b = -5, c = 3           b) b = -3, c = 5

 c)  b = -2, c = -15        d)  b = 2, c = -15

Solution

Problem 3 :

The distance d in meter traveled by a rocket depends on the amount of fuel f in liters, it burns according to the equation

d = 2f/3

Based on the table above, how many rockets traveled more than 20 meters ?

a)  One           b) Two     c) Three        d)  Four

Solution

Problem 4 :

g(x) = √(x - 1)(x- 2)

What is one possible value of x for which the function g above is undefined ?

Solution

Problem 5 :

Let the function f be defined by f(x) = 2x³ - 1 and let the function g be defined by g(x) = x² + 3, what is the value of f(g(1)) ?

a)  4      b)  23     c)  56    d)  127

Solution

Problem 6 :

Four values for the functions f and g are shown in the table above. If g(m) = 6, what is the value of f(m) ?

Solution

Problem 7 :

The graph of the function g in the xy plane is shown above. If f is another function defined in the same xy-plane and f(1) = 1, then g could be which of the following ?

a)  f - 1      b)  f - 2     c) f + 1      d) f + 2

Solution

Problem 8 :

f(x) = ax³ + b

In the function f defined above, a and b are constants. If f(-1) = 4 and f(1) = 10, what is the value of b ?

Solution

Problem 9 :

The function f is graphed in the xy plane above. If f(c) = f(3), which of the following could be the value of c ?

a)  -3       b)  -2       c) -1         d)  2

Solution

Problem 10 :

For all x ≥ 3,

f(x) = √(x - 3)/2. If f(n) = 3

what is the value of n ? 

Solution

Problem 11 :

The function f is defined by f(x) = 2x² - ax - 7, where a is constant. If the graph of f intersects the x-axis at (-1, 0), what is the value of a ?

a)  -9       b)  -5        c)  5         d)  9

Solution

Problem 12 :

If f(4) = -2, which of the following cannot be the definition of f ?

a)  f(x) = x - 6       b)  f(x) = x² - 4x - 2

c) f(x) = -3x + 14         d)  f(x) = -2(x - 3)²

Solution