For Problems 7 − 60 , graph each of the functions. (Objectives 2-5) f ( x ) = − 3 | x | − 4

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To determine To plot: The graph of the function f ( x ) = − 3 | x | − 4 . Explanation Approach: 1. The function f ( x ) = | x | will give f ( x ) = ± x . The absolute value is defined is defined for all real numbers as follows. 2. | x | = x , if x ≥ 0 3. | − x | = x , if x < 0 4. If f ( − x ) = f ( x ) , the function exhibits y -axis symmetry. 5. If f ( − x ) = − f ( x ) , the function exhibits origin symmetry. 6. The graph of f ( x ) = | x + k | + a , shifted k units rightwards if k > 0 or shifted | k | units leftwards if k < 0 in x -axis and shifted a units upwards if a > 0 or shifted | a | units downwards if a < 0 in y -axis. Calculation: Consider the given function, f ( x ) = − 3 | x | − 4 The given function is an absolute function. Substitute − x for x in the function, f ( − x ) = − 3 | − x | − 4 f ( − x ) = − 3 | x | − 4 From the above, it is clear that f ( − x ) = f ( x ) . The function exhibits y -axis symmetry. Therefore, the graph of the function f ( x ) = − 3 | x | − 4 shifted 4 units to the downwards. Substitute 0 for x in the function, f ( 0 ) = − 3 | 0 | − 4 f ( 0 ) = − 4 Therefore, the point ( 0 , − 4 ) is on the graph. Substitute 1 for x in the function, f ( 1 ) = − 3 | 1 | − 4 f ( 1 ) = − 3 − 4 f ( 1 ) = − 7 Therefore, the point ( 1 , − 7 ) is on the graph. Substitute − 1 for x in the function, f ( − 1 ) = − 3 | − 1 | − 4 f ( − 1 ) = − 3 − 4 f ( − 1 ) = − 7 Therefore, the point ( − 1 , − 7 ) is on the graph

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Intermediate Algebra

10th Edition

Jerome E. Kaufmann + 1 other

Publisher: Cengage Learning

ISBN: 9781285195728

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BuyFind

Intermediate Algebra

10th Edition

Jerome E. Kaufmann + 1 other

Publisher: Cengage Learning

ISBN: 9781285195728

Solutions

Chapter

Section

Answer 3

Solutions

Chapter

Section

Answer 4

Chapter

Section

Answer 5

To determine

To plot:

The graph of the function f(x)=−3|x|−4.

Explanation of Solution

Approach:

1. The function f(x)=|x| will give f(x)=±x. The absolute value is defined is defined for all real numbers as follows.

2. |x|=x, if x≥0

3. |−x|=x, if x<0

4. If f(−x)=f(x), the function exhibits y-axis symmetry.

5. If f(−x)=−f(x), the function exhibits origin symmetry.

6. The graph of f(x)=|x+k|+a, shifted k units rightwards if k>0 or shifted |k| units leftwards if k<0 in x-axis and shifted a units upwards if a>0 or shifted |a| units downwards if a<0 in y-axis.

Calculation:

Consider the given function,

f(x)=−3|x|−4

The given function is an absolute function.

Substitute −x for x in the function,

f(−x)=−3|−x|−4f(−x)=−3|x|−4

From the above, it is clear that f(−x)=f(x). The function exhibits y-axis symmetry. Therefore, the graph of the function f(x)=−3|x|−4 shifted 4 units to the downwards.

Substitute 0 for x in the function,

f(0)=−3|0|−4f(0)=−4

Therefore, the point (0, −4) is on the graph.

Substitute 1 for x in the function,

f(1)=−3|1|−4f(1)=−3−4f(1)=−7

Therefore, the point (1, −7) is on the graph.

Substitute −1 for x in the function,

f(−1)=−3|−1|−4f(−1)=−3−4f(−1)=−7

Therefore, the point (−1, −7) is on the graph

For Problems 7 − 60 , graph each of the functions. (Objectives 2-5) f ( x ) = − 3 | x | − 4

Intermediate Algebra

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Intermediate Algebra

For Problems 7 − 60 , graph each of the functions.

(Objectives 2-5)

f ( x ) = − 3 | x | − 4

Explanation of Solution

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