Practice Problems
Compare the graph of the given quadratic function f with the graph of y = x2.
1) f(x) = (x - 2)2 + 3
Determine if the function is even, odd, or neither.
2) f(x) = 2x5 + 2x3
Decide whether the relation defines a function.
3) {(-8, 2), (-8, 8), (-1, 8), (5, 6), (8, 7)}
5) y2 = 3x
Find the domain and range of the inverse of the given function.
7) f(x) = -4x - 2
Compute and simplify the difference quotient {f(x + h) - f(x)} / h, h ≠ 0.
8) f(x) = 7x - 9
Consider the function h as defined. Find functions f and g so that (f ° g)(x) = h(x).
9) h(x) = (8/x2) + 10
Find the requested value.
10) f(3) for f(x) = 3x + 1, if x < 1
f(3) for f(x) = 3x, if 3 ≤ x ≤ 8
f(3) for f(x) = 3 - 5x, if x > 8
Determine whether the function is symmetric with respect to the y-axis, symmetric with respect to the x-axis, symmetric with respect to the origin, or none of these.
11) f(x) = -5x3 + 2x
If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."
12) {(-2, 4), (-1, 4), (0, 1), (1, -5)}
If f is one-to-one, find an equation for its inverse.
13) f(x) = x3 - 5
Perform the requested operation or operations.
14) f(x) = √(x + 10), g(x) = 8x - 14
Find (f ° g)(x).
Graph the function.
16) f(x) = 4x + 2 if x < -2
f(x) = x if -2 ≤ x ≤ 3
f(x) = 3x-1 if x > 3
Find the indicated composite for the pair of functions.
18) (g ° f)(x): f(x) = (x - 3) / 6, g(x) = 6x + 3
Give the domain and range of the relation.
20) y = (x + 4)2 - 7