Unit 1A Test Review: Linear Functions

Domain Algebraically

100

What is the domain of y=7x⁶+7x-19? 

All real numbers 

200

What is the domain of the following function: 

f(x)=(x+3)/(2x-7)

All real numbers, except when x=7/2

300

Find the domain of f(x)=sqrt(5x-1)

The domain is all numbers greater than or equal to 1/5. 

400

Find the domain of the function h(x)=2*sqrt(4x+8)-1

The domain is all numbers greater than or equal to -2. 

500

Find the domain of the function g(x)=20*sqrt(-3x+6).

The domain is all numbers less than or equal to 2. 

Parallel, Perp., Coinciding

100

Determine if these lines are parallel, perpendicular, coinciding, or none:

y=(-2/5)x-7 and y=(2/5)x-7

None 

200

Determine if the lines are parallel, perpendicular, coinciding, or neither: 

4x-y=10 and x+4y=-28

Perpendicular 

300

Write down the slope(s) of the lines and identify whether they are parallel, perpendicular, or coinciding. 

3x-2y=5 and 6x-4y=10

Slope: (3/2)

Lines are parallel

400

Write down the slope(s) of the lines and identify whether they are parallel, perpendicular, or coinciding. 

y=5x-7 and 10x-2y=8

Slope of both lines: 5

Lines are parallel

500

Write down 2 lines that are coinciding to 

2x+3y=4

Answers vary; all coinciding lines are multiples of each other. Some answers include:

20x+30y=40, 6x+9y=12, and 10x+15y=20

Linear Equations

100

Write an equation of a line that has a y-intercept of -6 and a slope of 17.

y=-6x+17

200

DAILY DOUBLE!!!!!

Find the x and y intercepts of (2/5)x+4y=40

x-intercept: (100,0)

y-intercept: (0,10)

300

Find the x and y intercepts of 6x-9y=54. 

x-intercept: (9,0)

y-intercept: (0,-6)

400

Rewrite the following equation in slope-intercept form: 

-8x+3y=15

y=(8/3)x+5

500

Rewrite the following equation in slope-intercept form:

y-10=(2/3)(x+6)

y=(2/3)x+14

Writing Equations

100

Write the equation of a line that passes through the points (-1, 0) and (2, -5). (any form) 

y=(-5/3)(x+1)

y+5=(-5/3)(x-2)

y=(-5/3)x+10/3

200

Terrific Triple!!!! 

Write the equation of a line, in standard form, that passes through (-4,6) and (8,2)

(Recall that standard form is Ax+By=C)

(1/3)x+y=14/3

300

Write an equation of a line that is parallel to 5x-7y=3 and passes through (10, -7). 

y+7=(5/7)(x-10)

y=(5/7)x-(99/7)

400

Write an equation of a line, in slope-intercept form, that is perpendicular to x-3y=0 and passes through (-3, -5). 

y=-3x-14

500

Write an equation of a line, in slope-intercept form, that is perpendicular to 10x-5y=20 and passes through the origin. 

y=(-1/2)x

Misc.

100

What is the domain and range of the following relation, and is it a function? 

Q={(-2,5),(5,7),(-5,3),(2,7)}

Domain: {-5,-2,2,5}

Range: {3,5,7}

Yes, it is a function b/c each input has only 1 output

200

Given f(x)=x²-6x⁴-1, find f(2).

f(2)=-93

300

Given h(x)=8x³+3x²+4x-1, what value of x will make h(x)=14?

x=1

400

Suppose I have a graph of a relation that makes a heart. Is this a relation a function? Why or why not? (Do not have the vertical line test as your only reasoning)

It would not be a function because there are multiple inputs with multiple outputs. 

500

If I have f(x)=5x²-3x+7, what is f(x+3)? Make sure your answer is fully simplified. 

f(x+3)=5x²+27x+43