Misc.
Even, Odd or Neither?
4x2 -7
(hint: look at exponents)
Even
Determine and categorize the critical points:
-x3−3x2+2
(0, 2) relative maximum
(-2, -2) relative minimum
Evaluate at x=-2, 1, 4
x+1 x<0
f(x)= x2 0<x<3
5 x>3
f(-2)=-1
f(1)=1
f(4)=5
Find (f o g)(x)
f(x)=2x−1, g(x)=x2
(f o g)(x)=2x2-1
Find (f+g)(x) and its domain
f(x)=x2+1, g(x)=2x−3
(f+g)(x)=x2+2x−2
Domain: all real numbers
Even, Odd or Neither? Determine algebraically.
f(x)=5x5-2x
Odd
f(-x)=-5x5+2x
Determine the intervals on which the function is increasing and/or decreasing:
x3−3x2
Increasing: (−∞,0)∪(2,∞)
Decreasing: (0,2)
Evaluate at x=0, 2, 3
-x x<1
f(x)= 2x-1 x>1
f(0)= 0
f(2)= 3
f(3)= 5
Find (f o g)(x)
f(x)=x+5, g(x)=3x−2
(f o g)(x) = (3x-2)+5
= 3x+3
Find (f⋅g)(x) and its domain
f(x)=x2+1, g(x)=2x−3
(f⋅g)(x)=(x2+1)(2x−3)
= 2x3−3x2+2x−3
Domain: all real numbers
Find the intercepts of
f(x)=x2−6x+5
x-intercepts: 1, 5
y-intercept: f(0)=5
Describe the end behavior of the function:
f(x)=−x5+2x3
x→∞, f(x)→ −∞
x→−∞, f(x)→∞
Evaluate at x=-1, 1, 3
x2+2 x<0
f(x)= x2 0<x<2
4x x>2
f(-1)= 3
f(1)= 1
f(3)= 12
Find f(x) and g(x) such that (h)(x)=(4x−5)3
f(x)=x3
g(x)=4x-5
Find (f+g)(x) and its domain
f(x)=x−4, g(x)=x2+2
(f+g)(x)=x2+x−2
Domain: all real numbers
Determine and categorize the critical points:
f(x)=x2-4x+3
(2, -1) absolute minimum
Determine and identify any discontinuities:
h(x)= 1 / (x+1)(x-3)
Infinite discontinuity at x= -1, 3
Find f(x) and g(x) such that h(x)=(x+2)2−1
f(x)=x2-1
g(x)=x+2
Find (g-f)(x) and its domain
f(x)=2x+1, g(x)=x2−5
(g-f)(x)=x2-2x-6
Domain: all real numbers
Find the intercepts of
f(x)=x2−9
x-intercepts: -3, 3
y-intercept: f(0)= -9
Describe the end behavior of the function:
f(x)=4x4−x
x→∞, f(x)→∞
x→ -∞, f(x)→∞
Find (f o g)(x)
f(x)=x2, g(x)=x+3
(f o g)(x)=(x+3)2
= x2+6x+9