Inequalities
Solve the inequality:
3x-7>11
x>6
What is the parent function.
f(x) = (x-3)2 +4
x2
A graph is symmetric about the y‑axis. Is the function even, odd, or neither?
Answer: Even
If
f(x)=2x−3, g(x)=x2+1,
find (f+g)(2).
Answer: (f+g)(2)=(2⋅2−3)+(22+1)=1+5=6
|x-5| = 7
x=12,-2
Solve:
(5-2x)/3 > (x+7)/6
x<3/5
Describe all transformations:
h (x) = -2|x+1|
Shift left 1
vertical stretch factor of 2
reflection across x-axis
A function satisfies f(−x)=−f(x). What type of function is it?
Answer: Odd
Given
f(x)=x+4, g(x)=3x−2,
find the domain of (f−g)(x).
Answer: x≥−4
Solve:
|2x+3|<5
-4<x<1
Solve:
(3x-8)/4 + 2 <= (x+10)/2
x<=20
Transform the graph. Shift right 2, up 1, reflected across the x-axis.
f(x) = x3
f(x) = -(x-2)3 +1
Determine whether
f(x)=x3−4x
is even, odd, or neither.
Answer: Odd
f(x)=x2−9, g(x)=x−3,
compute f(x)/g(x) and simplify. Then determine the restricted value.
Answer: (x2−9)/(x−3) = x+3, x≠3
|3x-1| = |x+5|
x= 3, -1
Solve:
-15<=3(2-x)<9
-1<x<=7
A graph of y=∣x∣ is shifted right 5, down 3, and vertically stretched by 4. Write the transformed function.
f(x)=4∣x−5∣−3
A graph shows a function increasing on (−∞,−2), decreasing on (−2,5), and increasing again on (5,∞). What are the local extrema?
Answer: Local max at x=−2; local min at x=5
f(x)=2x/(x−1), g(x)=(x+3)/x,
Find (f of g)(x)
f(g(x))=(2x+6)/3, x/=0
|x+2|>=|x-6|
x>=2
Solve:
3x+2<-4 or 5-x>=12
x<-2
The graph of y=x is reflected across the x‑axis and shifted left 2. Write the new function.
f(x)=−sqrt(x+2)
Evaluate
f(x)={x2−4 x<1
3x+2 x≥1}
at x=1.
Answer: f(1)=5
h(x)=sqrt(2x+7)
decompose into h=f of g
g(x) = 2x+7, f(x) = sqrt(x)
Solve:
|3x+1|−4<5.
-10/3 < x < 8/3