Midterm Review

Things to Remember (5 Points)

1

This 2015 children's movie is about dealing with emotions, also the way that we read function composition.

Inside Out

2

When factoring, the first step is to look for a...

Greatest Common Factor (GCF)

3

An equation for which each x-value in the domain will produce exactly one y-value.

Function

4

The zeros of a polynomial are the ________________ of the equation or the x-intercepts of the graph.

roots/solutions

5

This formula can help us solve quadratics (it always works!).

Write the name of the formula, as well as the formula itself.

Quadratic Formula

Factoring (10 Points)

1

#20 Factor 𝑥² − 64 = 0 

(x+8)(x-8)

2

#21 Factor 124 = 𝑥² + 3 

(x+11)(x-11)

3

#22 Factor 9𝑥² + 6𝑥 = −1 

(3x+1)²

4

#23 Factor 3𝑥² + 2𝑥 = 21 

(3x-7)(x+3)

5

#24 Factor 6𝑥² − 2𝑥 = 0 

2x(3x-1)

Simultaneous Equations (10 Points)

1

#1 Solve the following pairs of simultaneous equations. 

𝑥 + 𝑦 = 7    and    𝑥² + 𝑦² = 25

(4,3) and (3,4)

2

#2 Solve the following pairs of simultaneous equations. 

𝑥 + 2𝑦 = 3   and   𝑥²+ 𝑥𝑦 = 2

(-4, 7/2) and (1, 1)

3

#3 Solve the following pairs of simultaneous equations. 

𝑦 = 2 − 𝑥    and   𝑥² − 𝑦² = 8

(3, -1)

4

#4 Solve the following pairs of simultaneous equations. 

4𝑥 + 3𝑦 = 25   and   𝑥² + 𝑦² = 25

(4, 3)

Function Composition (10 Points)

1

#5 Given 𝑓(𝑥) = 2𝑥² − 3, 𝑥 ≥ 0 and 𝑔(𝑥) = 3𝑥 − 1 

Find fg

18x²-12x-1

2

#6 Given 𝑔(𝑥) = 3𝑥 − 1 and ℎ(𝑥) = 𝑥+2/3 

Find gh

x+1

3

#7 Given 𝑓(𝑥) = 2𝑥² − 3, 𝑥 ≥ 0

Find ff

8x⁴-24x²+15

4

#8 Given ℎ(𝑥) = 𝑥+2/3 

Find h^-1(x)

3x-2

5

#9 Given 𝑓(𝑥) = 2𝑥² − 3, 𝑥 ≥ 0

Find f^-1(x)

square root of (x+3/2)

Extra Problems

1

#10 Given 𝑗(𝑥) = 1/𝑥−2 , 𝑥 ≠ 2 

Find j^-1(x)

1/x   +2

2

#25 Factor 20𝑥² = −25𝑥 

5x(4x+5)