2.4E: Exercises

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Practice makes perfect!

Graphs of linear functions

Graph the following linear functions:

\(f(x) = 4x - 4\)
\(f(x) = \frac{3}{2}x + 1\)
\(f(x) = -2x - 3\)
\(f(x) = -\frac{1}{3}x + 2\)
\(f(x) = 2\)
\(f(x) = -1\)

Answer

Graphs of absolute value functions

Graph the absolute value functions below:

\(f(x) = |x| + 2\)
\(f(x) = |x| - 3\)
\(f(x) = |x - 1|\)
\(f(x) = |x + 5|\)
\(f(x) = 2|x + 3| - 1\)
\(f(x) = -|x| + 4\)

Answer

Graphs of quadratic functions

Graph the following quadratic functions

\(f(x) = x^2 + 4\)
\(f(x) = \frac{1}{2}x^2 - 3\)
\(f(x) = (x - 3)^2 \)
\(f(x) = 2(x + 1)^2\)
\(f(x) = (x - 3)^2 + 4\)
\(f(x) = -(x + 2)^2 +5\)

Answer

Graphs of square root functions

Graph the following square root functions:

\(f(x) = \sqrt{x} - 1\)
\(f(x) = -2\sqrt{x} + 3\)
\(f(x) = \sqrt{x + 4}\)
\(f(x) = \sqrt{-x - 3}\)
\(f(x) = 2\sqrt{x + 1} - 2\)
\(f(x) = 3\sqrt{x - 2} - 4\)

Answer

Graphs of quotient functions

Graph the following quotient functions:

\(f(x) = \frac{1}{x} + 2\)
\(f(x) = \frac{2}{x} - 3\)
\(f(x) = \frac{1}{x + 4}\)
\(f(x) = -\frac{1}{x - 1}\)
\(f(x) = \frac{1}{x + 3} - 2\)
\(f(x) = \frac{3}{x - 2} + 1\)

Answer

Classifying functions based on their rule

Classify the following functions according to their family:

\(f(x) = x + 2\)
\(f(x) = x^2 - 4\)
\(f(x) = \frac{1}{3 + x}\)
\(f(x) = x^2 - 3x + 4\)
\(f(x) = \sqrt{x + 3} - 4\)
\(f(x) = -2|x - 3|\)

Answer

Linear
Quadratic
Quotient
Quadratic
Square root
Absolute value

Classifying functions based on their graphs

Classify the functions represented by the graphs below by family:

Answer

Linear
Quadratic
Quotient
Quadratic
Square root
Absolute value

Identify graphs of functions based on "basic shape"

Match the graphs below to the function it might represent based on its family.

Graph

Function

42.

$fam_graph1.JPG$

a.

\(f(x) = x^2 - 3x + 4\)

43.

$fam_graph11.JPG$

b.

\(f(x) = x + 2\)

44.

$fam_graph3.JPG$

c.

\(f(x) = -5\)

45.

$fam_graph4.JPG$

d.

\(f(x) = \frac{1}{3 + x}\)

46.

$fam_graph5.JPG$

e.

\(f(x) = -2|x - 3|\)

47.

$fam_graph6.JPG$

f.

\(f(x) = \sqrt{x + 3} - 4\)

Answer

b
c
d
a
f
e

Identify graphs of functions based on their "basic shape"

Match each function below to its possible graph based on its family.

Function

Graph

48.

\(f(x) = \sqrt{x - 3}\)

a.

$fam_funct4.JPG$

49.

\(f(x) = 4\)

b.

$fam_funct5.JPG$

50.

\(f(x) = (x + 5)^2\)

c.

$fam_funct1.JPG$

51.

\(f(x) = \frac{1}{2x + 3} - 4\)

d.

$fam_funct3.JPG$

52.

\(f(x) = \frac{1}{2}|x + 3| - 5\)

e.

$fam_funct6.JPG$

53.

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

f.

$fam_funct2.JPG$

Answer

c
f
d
a
b
e