Functions! Sections 2.3, 2.4, 2.5, 1.1

Function T/F

100

Is this relation a function?

{(1,2), 2,3), (3,4)}

Yes-each input has exactly one output.

200

Is this relation a function?

{(0,5), (0,7), (1,8)}

No-input 0 has 2 different outputs.

300

Is this a function?

x=4

No-this is a vertical line, which fails the vertical line test. It has an infinite number of outputs per single input.

400

Is this a function?

y=sqrt(x-2)

yes-There is exactly one output per input and passes the vertical line test.

500

Is this a function?

(x-4)² + (y+2)² = r²

No-This is a circle and has more than one output per input and fails the vertical line test.

Domain or Range

100

What is the domain and range of this relation?

{(1,4), (2,5), (3,6)}

Domain = {1, 2, 3}

Range = {4, 5, 6}

200

What is the domain and range?

f(x) = 3x + 2

Domain = all real numbers

Range = all real numbers

300

Find the domain and range. Interval notation.

f(x) = sqrt(x-1)

Domain = [1, infinity)

Range = [0, infinity) 

400

For what values of x is function defined, and what is the possible outputs?

f(x) = 5/(x-2) 

Domain: All real numbers except x=2

Range: all real numbers except y=0

500

What are the vertical and horizontal asymptotes of the function. 

f(x) = 5/(x-2)

Vertical asymptotes: x=2

Horizontal asymptotes: y=0

Intercepts and Slopes

100

Find the slope and y-intercepts. Answer in ordered pair.

y=3x+2

Slope = 3

y-intercept = (0,2)

200

Find the x-intercept. Ordered pair.

y= -2x + 6

x-intercept = (3,0)

300

Find the slope, x-intercept, and y-intercept. Ordered pair.

y = 0.5x - 4

Slope = 1/2

y-intercept = (0,4)

x-intercept = (8,0)

400

Find the slope of a line that passes through the points (1,2), (3,4)

m=1

500

Find the slope, x and y intercepts. Ordered pairs.

2x - 3y = 12

Slope: 2/3

y-intercept: (0, -4)

x-intercept: (6, 0)

Solving Linear and Rational Equations

100

Solve for x

2x + 5 = 15

x=5

200

Solve

x/3 - 4 = 2

x=18

300

Solve.

3(x - 4) = x² - 5x + 6

x = 3 or x = 6

400

Determine the restricted values:

4x/(x - 3) = (2x - 6)/(x + 1)

x is 3 

x is -1

500

Solve:

4x/(x - 3) = (2x - 6)/(x + 1)

x = -9

x = 1

Determine the Function

100

A line has slope m=3 and passes through the point (2,5). Write the equation of the function in slope-intercept form.

y = 3x - 1

200

Find the equation of the line that passes through (1, 4) and (3, 10).

y = 3x+1

300

a line has slope m = -2 and passes through the point (-3, 7). Write the equation in standard form.

2x + y = 1

400

What is the slope of the function x = 5/2?

Undefined

500

A line passes through the points (4, -1) and (10, 2). Find the equation of the line in slope-intercept, point-slope, and standard form.

y = 0.5x - 3

x - 2y = 6

y + 1 = 1/2(x - 4)