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Absolute Value Functions

This document provides examples of absolute value functions and asks students to: 1) Find x- and y-intercepts and sketch graphs of various absolute value functions. 2) Determine the domain and range of additional absolute value functions. 3) Solve equations involving absolute value functions graphically. The document contains multiple parts with examples of absolute value functions and asks students to analyze properties and solve related problems for practice with these types of functions.

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JohnnyLuanKhaiTuan
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171 views4 pages

Absolute Value Functions

This document provides examples of absolute value functions and asks students to: 1) Find x- and y-intercepts and sketch graphs of various absolute value functions. 2) Determine the domain and range of additional absolute value functions. 3) Solve equations involving absolute value functions graphically. The document contains multiple parts with examples of absolute value functions and asks students to analyze properties and solve related problems for practice with these types of functions.

Uploaded by

JohnnyLuanKhaiTuan
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Exercise 7.

02 Absolute value functions


1 Find the x- and y-intercepts of the graph of each function.
a f (x) = |x| + 7 b f (x) = |x| − 2 c y = 5|x|
d f (x) = −|x| + 3 e y = |x + 6| f f (x) = |3x − 2|
g y = |5x + 4| h y = |7x −1| i f (x) = |2x| + 9

2 Sketch the graph of each function.


a y = |x| b f (x) = |x| + 1 c f (x) = |x| − 3
d y = 2|x| e f (x) = −|x| f y = |x + 1|
g f (x) = −|x − 1| h y = |2x − 3| i f (x) = |3x| + 1

3 Find the domain and range of each function.


a y = |x − 1| b f (x) = |x| − 8 c f (x) = |2x + 5|
d y = 2|x| − 3 e f (x) = −|x − 3|

4 Solve each equation graphically.


a |x| = 3 b |x + 2| = 1 c |x − 3| = 0
d |2x − 3| = 1 e |2x + 3| = 11 f |5b − 2| = 8
g |3x + 1| = 2 h 5 = |2x + 1| i 0 = |6t − 3|
Exercise 7.02
1 a No x-intercepts, y-intercept 7 2 a y
b x-intercepts ±2, y-intercept –2 5
c x-intercept 0, y-intercept 0 4
d x-intercepts ±3, y-intercept 3 3
e x-intercept –6, y-intercept 6 2
y = |x|
2 1
f x-intercept , y-intercept 2
3
4 −4 −3 −2 −1 1 2 3 4 5 x
g x-intercept − , y-intercept 4 −1
5
−2
1
h x-intercept , y-intercept 1
7
i No x-intercepts, y-intercept 9

b y f y
5 5
4 4
3 y = |x| + 1 3
2 2
1 1 y = |x + 1|

−4 −3 −2 −1 1 2 3 4 5 x −4 −3 −2 −1 1 2 3 4 5 x
−1 −1
−2 −2

c f (x) g f (x)
3 2
2 1
1
−4 −3 −2 −1 1 2 3 4 5 x
−1
−4 −3 −2 −1 1 2 3 4 5 x
−1 −2
−2 f (x) = |x| − 3 −3
f (x) = −|x − 1|
−3 −4
−4 −5
d y h y
5 5
4 4 y = |2x − 3|
3 y = 2|x| 3
2 2
1 1

−4 −3 −2 −1 1 2 3 4 5 x −4 −3 −2 −1 1 2 3 4 5 x
−1 −1
−2 −2

e f (x) i f (x)
2 5
1 4
3
−4 −3 −2 −1 1 2 3 4 5 x f (x) = |3x| + 1
−1 2
−2 1
f (x) = −|x|
−3
−4 −3 −2 −1 1 2 3 4 5 x
−4 −1
−5 −2

3 a Domain (–∞, ∞), range [0, ∞)


b Domain (–∞, ∞), range [–8, ∞)
c Domain (–∞, ∞), range [0, ∞)
d Domain (–∞, ∞), range [–3, ∞)
e Domain (–∞, ∞), range (–∞, 0]

4 a x = ±3 b x = –1, –3 c x=3
d x = 1, 2 e x = 4, –7 f b = 2, –1.2
1 1
g x = , –1 h x = 2, –3 i t=
3 2

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