Semester Exam Review

Transformations

100

If P(3,−4) is on f(x) , what point lies on
g(x)=f(x−2)?

A. (1, –4)

200

If P(−1,6)is on f(x), find the point on g(x)=−f(x+4).

(-5, -6)

300

Describe the transformation from f(x)=(x+7)-3

Left 7, down 3

400

Describe the transformation from f(x)=x² to  f(x)=3x²+5

Vertical stretch by 3, up 5

500

Give the point mapping rule for g(x)=2f(x+1)−4

(What is happening to the x and y)

(x,y)→(x−1,2y−4)  

Trig Identities

100

If tan⁡θ=3/4, find sin⁡θ

3/5

200

If cot⁡θ=7/24 find csc⁡θ

25/7

300

Evaluate cos⁡(120∘)

-1/2

400

Evaluate sin⁡(5π/6)

−Squre root 3/2

500

Simplify sin⁡(arctan⁡(x)

x/1+x²

Function Composition

100

Find f(g(x)) for f(x)=2x  and g(x)=x+3

2x+6

200

Find g(f(x)) for f(x)=x²  and g(x)=3x

3x²

300

Find f(g(x)) for f(x)=∣x∣ f(x)=|x| and g(x)=x−4

∣x−4∣

400

Find g(f(x))  for f(x)=2x+3 and g(x)=x².

(2x+3)²

500

Find f(g(x)) for f(x)=3x−1 and g(x)=x²+2.

3x²+5

LOGS & INVERSES

100

Condense log⁡x+log⁡5

log(5x)

200

Expand log⁡₃(27x²)

log₃27+2log⁡₃x

300

Solve log⁡₂(x−1)=4

17

400

Find the inverse of f(x)=5x−7

f^-1(x)=x+7/5

500

Rewrite as one log: 3log⁡x+log⁡(2)+log(⁡43)

log(86x³)

GRAPHS & ASYMPTOTES

100

State the domain of f(x)=log⁡(x−3)

(3,∞)

200

Describe the polynomial with roots –2 multiplicity of 1, 1 multiplicity of 2, and 4 multiplicity of 3

Answer: Crosses at –2, bounces at 1, crosses at 4

300

Give a rational function with vertical asymptotes at –1 and 2

f(x)=1/(x+1)(x−2)

400

Write a cosine equation with amplitude 3 and period π

y=3cos⁡(2x)

500

Give a rational function with asymptotes at x=4, x=1

f(x)=1/(x−4)(x+1)