Math 3A - Chapter 2 Exam Review

Ordered pairs(2.1-2.3)

100

What are the x-intercept and y-intercept of the graph of: 

3x+7y=21

x-intercept: (7,0)

y-intercept: (0,3)

200

Create a table of values with 3 ordered pairs and graph the equation:

y=x²-8          Use: -2,0,2 as your x-values

Ordered pairs: (-2,-4),(0,0),(2,-4)

Graph is an upside down parabola with Vertex @ (0,0)

300

Find the x-intercepts of: y=x²-9

x-intercepts: (3,0),(-3,0)

400

Find 3 ordered pairs for the equation and graph:

y=|x-8|

use -2,8,13 as the x-values

ordered pairs: (-2,10),(8,0),(13,5)

The graph is a v-shaped graph with vertex @ (8,0)

500

If a vertical line is drawn through the point (-2,3), at what point will it intersect the x-axis?

*Might be helpful to sketch the graph*

It will intersect at point: (-2,0)

Relations and Functions(2.3)

100

Does the relation define a function?

{(5,3),(2,3),(3,4)}

Yes it is a function. Each x-value is different

200

Is y=x¹³ a function? Give domain and range

Yes y=x¹³ is a function. 

Domain: (-∞,∞)

Range: (-∞,∞)

300

let h(x)=-x²+6x+2; Find and simplify h(-3)

h(-3)=-25

400

Is y=√5x+1 a function? 

**5x+1 is under √**

Yes y=√5x+1 is a function.

500

Let f(x)={(6,3),(-1,6),(-3,7)};  Find f(6)

f(6)=3

Linear Functions(2.4-2.5)

100

Find the slope of the line containing (-5,3) and (8,4)

m= 1/13

200

Find the slope of the line: Horizontal, through (6,2)

m=0

*Horizontal line always 0 slope*

300

Write an equation in slope-intercept form. 

Through (6,8) and parallel to y=-8

*might be helpful to use the Point-slope formula*

Slope-intercept form: y=8

400

Write an equation in slope-intercept form:

Through (-1,5) and parallel to x+2y=5

*might be helpful to put equation in slope-int form first then use the point-slope formula*

slope-intercept form: y=(-1/2)x+9/2

500

Write an equation in slope-intercept form:

Through (1,6) and perpendicular to 2x+5y=1

slope intercept form: y= (5/2)x+7/2

Parent Graphs(2.6-2.7)

100

Give the shape, key point (vertex, starting point, center), Domain and Range and also the Transformations of Function equation of:

y=|x|

V-shaped

Vertex (h,k)

Domain (-∞,∞)

Range [0,∞)

f(x)=a|x-h|+k

200

Give the shape, key point (vertex, starting point, center), Domain and Range and also the Transformations of Function equation of:

y=x²

U-shaped

vertex (h,k)

Domain: (-∞,∞)

Range: [0,∞)

f(x)=a(x-h)²+k

300

Give the shape, key point (vertex, starting point, center), Domain and Range and also the Transformations of Function equation for:

y=x³

1/2 up-1/2 down parabola

Point of inflection (h,k)

Domain: (-∞,∞)

Range: (-∞,∞)

f(x)=a(x-h)³+5

400

Give the shape, key point (vertex, starting point, center), Domain and Range and also the Transformations of Function equation for:

y=√x

Half sideways parabola

Starting point (h,k)

Domain: [0,∞)

Range: [0,∞)

f(x)=a(√x-h)+k 

500

Is this a function? Why or Why not?

x=y²

Not a function because it Does NOT pass the vertical line test. 

Composition of Functions(2.8)

100

let f(x)=x²-5 and g(x)=1-x;   Find (f/g)(-10)

(f/g)(-10)= 95/11

200

let f(x)=2x²+2 and g(x)=-3x+3;  Find (f-g)(-4)

(f-g)(-4)=19

300

let f(x)=x²-5 and g(x)=15-x; Find (fg)(-6)

(fg)(-6)=651

400

Let f(x)=x+2 and g(x)=x²; Find (GoF)(1)

(GoF)(1)=9

500

let f(x)=4x-2 and g(x)=1/4(x+2)

find (gof)(x) and (fog)(x)

Then determine if (fog)(x)=(gof)(x)

(fog)(x)=x

(gof)(x)=x

Yes they = each other