Chapter 1
Evaluate f(-3).
f(x) = 3x2 - 8x + 9
f(-3)= 60
Find (f + g)(x).
f(x) = 6x2 - 9x + 1
g(x) = 4x + 8
(f + g)(x) = 6x2 - 5x + 9
Solve.
square root (x - 3) = 5
x = 28
Classify the polynomial as constant, linear, quadratic, cubic, or quartic.
f(x) = 4x - 7x2 + 9x3
Cubic
Find the inverse of the function.
f(x) = 1/2x - 9
f-1(x) = 2x + 18
Determine whether or not the relation is a function.
{(5, 1), (7, 1), (-1, 0), (-7, 5)}
Yes
Find (f - g)(x).
f(x) = 7x - 9
g(x) = x2 - 8x - 1
(f - g)(x) = -x2 + 15x - 8
(2 + 8i)(3 - 9i)
78 + 6i
Find the zeros of the polynomial and state the multiplicity of each.
f(x) = 3(x - 1)4(x + 3)2
x = 1 multiplicity of 4
x = -3 multiplicity of 2
log28
3
State the center and radius of the circle.
(x - 7)2 + (y + 5)2 = 4
Center (7, -5)
r = 2
Find f(g(x)).
f(x) = x2 - 5x
g(x) = x + 2
f(g(x)) = x2 - x - 6
Solve.
|x - 3| = 10
x = 13, - 7
Use synthetic division to determine whether -2 is a zero of the polynomial.
f(x) = -6x3 + x2 - 8x - 6
No
Convert to a logarithmic equation.
53 = 125
log5125 = 3
Find the slope of the line given the points.
(-5, 8) and (-5, 10)
Undefined
Write an equation of a radical function that is reflected across the x-axis, translated left 4 and up 8.
f(x) = - (sqrt(x + 4)) + 8
Solve by factoring.
4x2 - 4x - 3 = 0
x = 3/2, -1/2
Find any vertical asymptotes.
f(x) = 4/(x2 - 25)
x = 5
x = -5
Solve.
log2(4x - 1) = 3
x = 9/4
Find the zero of the function.
f(x) = 3 - 7x
x = 3/7
If q varies inversely with r, and q is -8 when r is 3, write the inverse variation equation.
q = -24/r
Solve.
(x + 5)/2 + (x - 3)/5 = 41/5
x = 9
List the critical values. Then solve the inequality. Write your answer in interval notation.
x/(x+2) > 0
Critical value = -2
(-infinity, -2) U (0, infinity)
Solve.
ln (x + 1) = ln 2 - ln x
x = 1