Essential Question: Wait… didn’t we see this stuff before?

Find all solutions: |x2 + 8x + 14| = 2 Create two equations

The solution is c

2

2

2

1) 8 14 2

8 14 2

8 12 0

( 6)( 2)

6 or 2

2

0

2

x x

x x

x x

x x

x x

2

2

2

2) 8 14 2

8 14 2

8 16 0

( 4)( 4) 0

o

2 2

4 r 4

x x

x x

x x

x x

x x

Write 2 < x < 8 in interval notation

If an inequality has a line underneath it, we use braces; parenthesis without.

(2, 8]

Solve the inequality and express your answer in interval notation: -15<-3x+3<-3

[2, 6] The answer is a

3 3 3

3

15 3 3 3

18 3 6

6 2

2 6

3 3

x

x

x

x

Determine the domain of the function

The rule about domains are that they’re all real number except when taking square roots (not applicable) or dividing by 0.

To check the denominator, set it equal to 0.x(x2 – 81) = 0x = 0 or x2 – 81 = 0x = 0 or x2 = 81x = 0 or x = +9

The answer is a

2

2( )

( 81)

xh x

x x

5) Use the vertical line test Yeah… use the vertical line test All of the graphs fail the vertical line test,

except for a, which is your answer

6) Which function is in quadratic x-intercept form?

x-intercept form: a(x – s)(x – t) The only one that fits that mold is b, which is

your answer Remember:

Transformation form: a(x – h)2 + k Polynomial form: ax2 + bx + c

Your quarterly will ask you to identify one of the three

Find the rule and the graph of the function whose graph can be obtained by performing the translation 3 units right and 4 units up on the parent function f(x) = x2.

Horizontal effects (right/left) are inside parenthesis. Vertical effects (up/down) are outside parenthesis.

Inside stuff works opposite the way you’d expect. Outside works normal.

f(x) = (x – 3)2 + 4 The answer is c

f(x) = x5 & g(x) = 4 – x. Find (g o f)(x)Take x, plug it into the closest function (f)

f(x) = x5

Take that answer, plug it into the next closest function (g) g(x5) = 4 – x5

The answer is c Ignore the note about domains, but do

make sure when the quarterly comes, you pay attention to order. Answer a is (fg)(x) Answer b is (f + g)(x) Answer d is (f o g)(x)

Find all solutions: 2 13 72 6x x

2

22

2

2

13 72

13 72 36

9

13 36 0

( 9)( 4

or 4

6

3 6

)

3

0

6

x x

x x

x x

x x

x x

Find all real solutions:

Real solutions? When numerator = 0 x2 + x - 42 = 0 (x - 6)(x + 7) = 0 x = 6 or x = -7

I’m only asking for real solutions, so just test your real solutions in the denominator to make sure they’re not extraneous (denominator = 0). (6)2 + 16(6) + 63 = 195 (works) (-7)2 + 16(-7) + 63 = 0 (extraneous)

Real solution: 6

2

2

420

16 63

x x

x x

Solve the inequality and express your answer in interval notation:

Critical Points Real solutions: 5 & -9 Extraneous solution: 4

Test the intervals (-∞, -9] use x = -10, get -15/14 > 0FAIL [-9, 4) use x = 0, get 11.25 > 0 PASS (4, 5] use x = 4.5, get -13.5 > 0 FAIL [5, ∞) use x = 6, get 7.5 > 0

PASS Interval solutions are [-9, 4) and [5, ∞)

( 5)( 9)0

( 4)

x x

x

Find the selected values of the function

Check each input to decide which function it should be plugged into (top or bottom)a) f(-1) [bottom function], -8 + 7(-1)2 = -1b) f(0) [top function], ⅓(0) = 0c) f(1) [top function], ⅓(1) = ⅓d) f(-1.9) [bottom function], -8 + 7(-1.9)2 =

17.27

13

2

if x > -1( )

8 7 if x -1

xf x

x

Tired of this question yet? For parts a & b, find the value

along the x-axis, and determine the y-value(find the output tomatch the input)

f(0) = 4 f(-1) = 0 (use the closed dot) Domain (x-values) = [-5, 5) Range (y-values) = [-4, 4] (the peak

counts)

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

Determine the x-intercepts and vertex of the functionf(x) = x2 + 12x + 36

x-intercepts are found using the quadratic equation, or factoring (x + 6)(x + 6). There is only one x-intercept: -

6 The vertex is at

1st coordinate: (-12)/2(1) = -6 2nd coordinate, plug in: (-6)2 + 12(-6) + 36 =

0 Vertex is at (-6, 0)

,2 2

b bf

a a

f(x) = 16 – x2, g(x) = 4 – x.Find (f – g)(x) and its domain

Subtract the second function from the first. Make sure to use parenthesis around the function. [16 – x2] – [4 – x] (distribute the negative

sign)16 - x2 – 4 + x (combine like terms, put in

order) -x2 + x + 12Domain of f is all real numbers. Domain of g is

also all real numbers. The domain of the added function is all real numbers.

Find the difference quotient: 2x2 – 3x – 8Function using (x+h) – function

using x

2 2

2 2 2

22

2

2

( ) ( )

2( ) 3( ) 8 2 3 8

2( 2

4

) 3 3 8 2 3 8

4 2 3

4 2

3 3

2 33

82 2 8

f x h f x

h

x h x h x x

h

x xh h x h x x

h

xh h h

h

xh h h

hh

x x xx

x