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Intermediate Algebra
Graphs of Equations, Inequalities, and Functions

1
Graphs of Equations

Problem  1
practice icon

Plot the ordered pairs (3,4), (3,4), (3,4), and (3,4).

Choose instructor to watch:
Molly S. cc
Molly S.
Preston cc
Preston
Betsy cc
Betsy
David cc espanol spanish
David
Problem  2
practice icon

Graph y=13x

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Betsy cc
Betsy
Preston cc
Preston
Mr. Martinez espanol spanish
Mr. Martinez
Problem  3
practice icon

Graph y=13x+2

Choose instructor to watch:
Lauren cc
Lauren
Preston cc
Preston
Betsy cc
Betsy
David espanol spanish
David
Problem  4
practice icon

Graph y=13x4

Choose instructor to watch:
Stefanie cc
Stefanie
Betsy cc
Betsy
Preston cc
Preston
Mr. Martinez espanol spanish
Mr. Martinez
Problem  5
practice icon

Graph the equation y=x2.

Choose instructor to watch:
Stefanie cc
Stefanie
Betsy cc
Betsy
Preston cc
Preston
Mr. Martinez cc espanol spanish
Mr. Martinez
Problem  6
practice icon

Graph y=x24

Choose instructor to watch:
Stefanie cc
Stefanie
Betsy cc
Betsy
CJ cc
CJ
Julieta cc espanol spanish
Julieta
Problem  7

Graph y=|x| and y=|x|4

Choose instructor to watch:
Stefanie cc
Stefanie
Betsy cc
Betsy
Preston cc
Preston
Mr. Martinez espanol spanish
Mr. Martinez
Problem  8
practice icon

Find the intercepts for y=x24.

Choose instructor to watch:
Stefanie cc
Stefanie
Betsy cc
Betsy
Preston cc
Preston
Mr. Martinez espanol spanish
Mr. Martinez
Problem  9
practice icon

Graph each of the following lines.

  1. y=12x

  2. x=3

  3. y=2

Choose instructor to watch:
Stefanie cc
Stefanie
Betsy cc
Betsy
Preston cc
Preston
Julieta espanol spanish
Julieta

2
Introduction to Functions

Problem  1
practice icon

Make a table and graph for y=7.5x for 0x40.

Choose instructor to watch:
Stefanie cc
Stefanie
Betsy cc
Betsy
Preston cc
Preston
Mr. Martinez cc espanol spanish
Mr. Martinez
Problem  2
practice icon

State the domain and range for y=7.5x, 0x40.

Choose instructor to watch:
Stefanie cc
Stefanie
Betsy cc
Betsy
Preston cc
Preston
Julieta cc espanol spanish
Julieta
Problem  3
practice icon

Graph x=y2

Choose instructor to watch:
Stefanie cc
Stefanie
Betsy cc
Betsy
CJ cc
CJ
Mr. Martinez cc espanol spanish
Mr. Martinez
Problem  4
practice icon
Choose instructor to watch:
Jesse
Jesse
Stefanie cc
Stefanie
CJ cc
CJ
Julieta cc espanol spanish
Julieta

3
Function Notation

Problem  1
practice icon

If f(x)=7.5x, find f(0), f(10), and f(20).

Choose instructor to watch:
Winston cc
Winston
Betsy cc
Betsy
Spencer cc
Spencer
Mr. Martinez cc espanol spanish
Mr. Martinez
Problem  2
practice icon

If it takes Lorena t minutes to run a mile, then her average speed is s(t)=60t. Find s(10) and s(8).

Choose instructor to watch:
Betsy cc
Betsy
Preston cc
Preston
Gordon cc espanol spanish
Gordon
Problem  3
practice icon

A painting is purchased for $125. If its value doubles every 5 years, then its value is V(t)=1252t5. Find V(5) and V(10)

Choose instructor to watch:
Breylor cc
Breylor
Stefanie cc
Stefanie
Winston cc
Winston
Mr. Martinez cc espanol spanish
Mr. Martinez
Problem  4

A balloon has the shape of a sphere with a radius of 3 inches. Use V(r)=43πr3 and S(r)=4πr2 to find the volume and the surface area.

Choose instructor to watch:
Aaron cc
Aaron
Stefanie cc
Stefanie
CJ cc
CJ
Julieta cc espanol spanish
Julieta
Problem  5
practice icon

If f(x)=3x2+2x1, find f(0), f(3), and f(2).

Choose instructor to watch:
Stefanie cc
Stefanie
Betsy cc
Betsy
Preston cc
Preston
Cynthia espanol spanish
Cynthia
Problem  6
practice icon

Is f(x)=4x1 and g(x)=x2+2, then find f(x) and g(x) when x=5, 2, 0, z, a, and a+3.

Choose instructor to watch:
Betsy cc
Betsy
Preston cc
Preston
Julieta cc espanol spanish
Julieta
Problem  7
practice icon

f={(2,0),(3,1),(2,4),(7,5)} find f(2), f(3), f(2), and f(7)

Choose instructor to watch:
Betsy cc
Betsy
Preston cc
Preston
Mr. Martinez espanol spanish
Mr. Martinez
Problem  8
practice icon

If f(x)=2x2 and g(x)=3x1, find f[g(2)] and g[f(2)]

Choose instructor to watch:
Betsy cc
Betsy
Preston cc
Preston
Julieta cc espanol spanish
Julieta

4
Algebra and Composition with Functions

Problem  1
practice icon

If f(x)=4x2+3x+2 and g(x)=2x25x6, find f+g, fg, fg, f/g.

Choose instructor to watch:
Betsy cc
Betsy
Preston cc
Preston
Julieta cc espanol spanish
Julieta
Problem  2
practice icon

Let f(x)=4x3, g(x)=4x27x+3, and h(x)=x1. Find f+g, fh, fg, and g/f.

Choose instructor to watch:
Betsy cc
Betsy
Preston cc
Preston
Julieta cc espanol spanish
Julieta
Problem  3

Let f(x)=2x4, g(x)=2x, and h(x)=x24. Find (f+h)(x), (fg)(x), and (fg)(x).

Choose instructor to watch:
Molly S. cc
Molly S.
Winston cc
Winston
Cynthia espanol spanish
Cynthia
Problem  4
practice icon

Let f(x)=4x3, g(x)=4x27x+3, and h(x)=x1. Find (f+g)(2), (fh)(1), (fg)(0), and (g/f)(5).

Choose instructor to watch:
Betsy cc
Betsy
Preston cc
Preston
Mr. Martinez cc espanol spanish
Mr. Martinez
Problem  5
practice icon

If f(x)=x+5 and g(x)=x22x, find (fg)(x) and (gf)(x)

Choose instructor to watch:
Molly S. cc
Molly S.
Betsy cc
Betsy
Preston cc
Preston
Octabio cc espanol spanish
Octabio
Problem  6

If f(x)=x+7, g(x)=1x, find (fg)(x) and (gf)(x)

Choose instructor to watch:
Molly S. cc
Molly S.
Octabio
Octabio
Cynthia espanol spanish
Cynthia

5
Slope and Average Rate of Change

Problem  1
practice icon

Find the slope of y=2x3

Choose instructor to watch:
Stefanie cc
Stefanie
Betsy cc
Betsy
Mr. Martinez cc espanol spanish
Mr. Martinez
Problem  2
practice icon

Find the slope of the line through (2,1) and (5,4).

Choose instructor to watch:
Betsy cc
Betsy
Preston cc
Preston
Molly S. cc
Molly S.
Mr. Martinez cc espanol spanish
Mr. Martinez
Problem  3
practice icon

Find the slope of the line containing (3,1) and (3,4)

Choose instructor to watch:
Stefanie cc
Stefanie
Betsy cc
Betsy
CJ cc
CJ
Cynthia cc espanol spanish
Cynthia
Problem  4

Let f(x)=x23x. Find the average rate of change of f(x) on the interval [1,3].

Choose instructor to watch:
Molly S. cc
Molly S.
Octabio
Octabio
Cynthia espanol spanish
Cynthia

6
Linear Functions

Problem  1
practice icon

Find the equation, and graph the line with slope 43 and y-intercept 5.

Choose instructor to watch:
Betsy cc
Betsy
Preston cc
Preston
Molly S. cc
Molly S.
Julieta cc espanol spanish
Julieta
Problem  2
practice icon

Find the slope and y-intercept for 2x+y=4.

Choose instructor to watch:
Betsy cc
Betsy
Preston cc
Preston
Mr. Martinez espanol spanish
Mr. Martinez
Problem  3
practice icon

Graph the linear function f(x)=23x+2

Choose instructor to watch:
Stefanie cc
Stefanie
CJ cc
CJ
Mr. Martinez cc espanol spanish
Mr. Martinez
Problem  4
practice icon

Find the equation of the line with slope 2 that contains the point (4,3).

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Preston cc
Preston
Betsy cc
Betsy
Mr. Martinez cc espanol spanish
Mr. Martinez
Problem  5
practice icon

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

Choose instructor to watch:
Betsy cc
Betsy
Preston cc
Preston
Octabio cc
Octabio
Octabio cc espanol spanish
Octabio
Problem  6
practice icon

Find the equation of the line through (1,4) and perpendicular to 2xy=3

Choose instructor to watch:
Stefanie cc
Stefanie
Betsy cc
Betsy
Preston cc
Preston
Stefanie cc
Stefanie

7
Linear Inequalities

Problem  1
practice icon

Graph x+y4

Choose instructor to watch:
Betsy cc
Betsy
Preston cc
Preston
Molly S. cc
Molly S.
Mr. Martinez espanol spanish
Mr. Martinez
Problem  2
practice icon

Graph y<2x3

Choose instructor to watch:
Betsy cc
Betsy
Preston cc
Preston
Molly S. cc
Molly S.
Mr. Martinez espanol spanish
Mr. Martinez
Problem  3
practice icon

Graph x5

Choose instructor to watch:
Betsy cc
Betsy
Preston cc
Preston
Molly S. cc
Molly S.
Mr. Martinez espanol spanish
Mr. Martinez