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Intermediate Algebra
Graphs of Equations, Inequalities, and Functions

1
Graphs of Equations

Problem 1

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 spanish language icon
David
Problem 2

Graph \(y=-\displaystyle\frac{1}{3}x\)

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Betsy cc
Betsy
Preston cc
Preston
Edwin spanish language icon
Edwin
Problem 3

Graph \(y=-\displaystyle\frac{1}{3}x+2\)

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

Graph \(y=-\displaystyle\frac{1}{3}x-4\)

Choose instructor to watch:
Stefanie cc
Stefanie
Betsy cc
Betsy
Preston cc
Preston
Edwin spanish language icon
Edwin
Problem 5

Graph the equation \(y=x^2\).

Choose instructor to watch:
Stefanie cc
Stefanie
Betsy cc
Betsy
Preston cc
Preston
Edwin cc spanish language icon
Edwin
Problem 6

Graph \(y=x^2-4\)

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

Graph \(y=\lvert x \rvert\) and \(y=\lvert x \rvert -4\)

Choose instructor to watch:
Stefanie cc
Stefanie
Betsy cc
Betsy
Preston cc
Preston
Edwin spanish language icon
Edwin
Problem 8

Find the intercepts for \(y=x^2-4\).

Choose instructor to watch:
Stefanie cc
Stefanie
Betsy cc
Betsy
Preston cc
Preston
Edwin spanish language icon
Edwin
Problem 9

Graph each of the following lines.

  1. \(y=\displaystyle\frac{1}{2}x\)

  2. \(x=3\)

  3. \(y=-2\)

Choose instructor to watch:
Stefanie cc
Stefanie
Betsy cc
Betsy
Preston cc
Preston
Julieta spanish language icon
Julieta

2
Introduction to Functions

Problem 1

Make a table and graph for \(y=7.5x\) for \(0\leq x \leq 40\).

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Stefanie cc
Stefanie
Betsy cc
Betsy
Preston cc
Preston
Edwin cc spanish language icon
Edwin
Problem 2

State the domain and range for \(y=7.5x\), \(0\leq x\leq 40\).

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Stefanie cc
Stefanie
Betsy cc
Betsy
Preston cc
Preston
Julieta cc spanish language icon
Julieta
Problem 3

Graph \(x=y^2\)

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Stefanie cc
Stefanie
Betsy cc
Betsy
CJ cc
CJ
Edwin cc spanish language icon
Edwin
Problem 4
example image
Choose instructor to watch:
Jesse
Jesse
Stefanie cc
Stefanie
CJ cc
CJ
Julieta cc spanish language icon
Julieta

3
Function Notation

Problem 1

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

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Winston cc
Winston
Betsy cc
Betsy
Spencer cc
Spencer
Edwin cc spanish language icon
Edwin
Problem 2

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

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Betsy cc
Betsy
Preston cc
Preston
Gordon cc spanish language icon
Gordon
Problem 3

A painting is purchased for \(\$125\). If its value doubles every \(5\) years, then its value is \(V(t)=125\cdot2^{\frac{t}{5}}\). Find \(V(5)\) and \(V(10)\)

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Breylor cc
Breylor
Stefanie cc
Stefanie
Winston cc
Winston
Edwin cc spanish language icon
Edwin
Problem 4

A balloon has the shape of a sphere with a radius of \(3\) inches. Use \(V(r)=\displaystyle\frac{4}{3}\pi r^3\) and \(S(r)=4\pi r^2\) to find the volume and the surface area.

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Aaron cc
Aaron
Stefanie cc
Stefanie
CJ cc
CJ
Julieta cc spanish language icon
Julieta
Problem 5

If \(f(x)=3x^2+2x-1\), find \(f(0)\), \(f(3)\), and \(f(-2)\).

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Stefanie cc
Stefanie
Betsy cc
Betsy
Preston cc
Preston
Cynthia spanish language icon
Cynthia
Problem 6

Is \(f(x)=4x-1\) and \(g(x)=x^2+2\), then find \(f(x)\) and \(g(x)\) when \(x=5\), \(-2\), \(0\), \(z\), \(a\), and \(a+3\).

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Betsy cc
Betsy
Preston cc
Preston
Julieta cc spanish language icon
Julieta
Problem 7

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

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Betsy cc
Betsy
Preston cc
Preston
Edwin spanish language icon
Edwin
Problem 8

If \(f(x)=2x^2\) and \(g(x)=3x-1\), find \(f[g(2)]\) and \(g[f(2)]\)

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Betsy cc
Betsy
Preston cc
Preston
Julieta cc spanish language icon
Julieta

4
Algebra and Composition with Functions

Problem 1

If \(f(x)=4x^2+3x+2\) and \(g(x)=2x^2-5x-6\), find \(f+g\), \(f-g\), \(fg\), \(f/g\).

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Betsy cc
Betsy
Preston cc
Preston
Julieta cc spanish language icon
Julieta
Problem 2

Let \(f(x)=4x-3\), \(g(x)=4x^2-7x+3\), and \(h(x)=x-1\). Find \(f+g\), \(fh\), \(fg\), and \(g/f\).

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Betsy cc
Betsy
Preston cc
Preston
Julieta cc spanish language icon
Julieta
Problem 3

Let \(f(x)=2x-4\), \(g(x)=\dfrac{2}{x}\), and \(h(x)=x^2-4\). Find \((f+h)(x)\), \((f\cdot g)(x)\), and \(\left(\dfrac{f}{g}\right)(x)\).

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Molly S. cc
Molly S.
Winston cc
Winston
Cynthia spanish language icon
Cynthia
Problem 4

Let \(f(x)=4x-3\), \(g(x)=4x^2-7x+3\), and \(h(x)=x-1\). Find \((f+g)(2)\), \((fh)(-1)\), \((fg)(0)\), and \((g/f)(5)\).

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Betsy cc
Betsy
Preston cc
Preston
Edwin cc spanish language icon
Edwin
Problem 5

If \(f(x)=x+5\) and \(g(x)=x^2-2x\), find \((f \circ g)(x)\) and \((g \circ f)(x)\)

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Molly S. cc
Molly S.
Betsy cc
Betsy
Preston cc
Preston
Octabio cc spanish language icon
Octabio
Problem 6

If \(f(x)=x+7\), \(g(x)=\dfrac{1}{x}\), find \((f\circ g)(x)\) and \((g\circ f)(x)\)

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Molly S. cc
Molly S.
Octabio
Octabio
Cynthia spanish language icon
Cynthia

5
Slope and Average Rate of Change

Problem 1

Find the slope of \(y=2x-3\)

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Stefanie cc
Stefanie
Betsy cc
Betsy
Edwin cc spanish language icon
Edwin
Problem 2

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

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Betsy cc
Betsy
Preston cc
Preston
Molly S. cc
Molly S.
Edwin cc spanish language icon
Edwin
Problem 3

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 spanish language icon
Cynthia
Problem 4

Let \(f(x)=x^2-3x\). Find the average rate of change of \(f(x)\) on the interval \([1,3]\).

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Molly S. cc
Molly S.
Octabio
Octabio
Cynthia spanish language icon
Cynthia

6
Linear Functions

Problem 1

Find the equation, and graph the line with slope \(-\dfrac{4}{3}\) and \(y\)-intercept \(5\).

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

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

Choose instructor to watch:
Betsy cc
Betsy
Preston cc
Preston
Edwin spanish language icon
Edwin
Problem 3

Graph the linear function \(f(x)=-\dfrac{2}{3}x+2\)

Choose instructor to watch:
Stefanie cc
Stefanie
CJ cc
CJ
Edwin cc spanish language icon
Edwin
Problem 4

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
Edwin cc spanish language icon
Edwin
Problem 5

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 spanish language icon
Octabio
Problem 6

Find the equation of the line through \((-1,\, 4)\) and perpendicular to \(2x-y=-3\)

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Stefanie cc
Stefanie
Betsy cc
Betsy
Preston cc
Preston
Edwin cc spanish language icon
Edwin

7
Linear Inequalities

Problem 1

Graph \(x+y\leq 4\)

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Betsy cc
Betsy
Preston cc
Preston
Molly S. cc
Molly S.
Edwin spanish language icon
Edwin
Problem 2

Graph \(y<2x-3\)

Choose instructor to watch:
Betsy cc
Betsy
Preston cc
Preston
Molly S. cc
Molly S.
Edwin spanish language icon
Edwin
Problem 3

Graph \(x\leq 5\)

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Betsy cc
Betsy
Preston cc
Preston
Molly S. cc
Molly S.
Edwin spanish language icon
Edwin