Question

For each of the following functions, first sketch the graph of its associated function, $f(x)=x^{2}, f(x)=x^{3},$ or $f(x)=|x|$ Then draw the graph of function $g$ using translations and/or a reflection. See Examples 7 and $8 .$ $$ g(x)=|x+4|+3 $$

Name: Problem 52, Chapter 8: Elementary and Intermediate Algebra
Uploaded: 2020-06-12T01:09:06-08:00
Duration: 59 s
Channel: Brandon Fox
Description: For each of the following functions, first sketch the graph of its associated function, f(x)=x^2, f(x)=x^3, or f(x)=|x| Then draw the graph of function g using translations and/or a reflection. See Examples 7 and 8 . g(x)=|x+4|+3

   For each of the following functions, first sketch the graph of its associated function, $f(x)=x^{2}, f(x)=x^{3},$ or $f(x)=|x|$ Then draw the graph of function $g$ using translations and/or a reflection. See Examples 7 and $8 .$
$$
g(x)=|x+4|+3
$$

Elementary and Intermediate Algebra

Alan S. Tussy, R.… 5th Edition

Chapter 8, Problem 52

Instant Answer

Solved by Expert Brandon Fox

06/12/2020

Step 1

The graph of this function is a V shape, with the vertex at the origin (0,0) and the arms of the V extending upwards to the right and left. Show more…

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For each of the following functions, first sketch the graph of its associated function, $f(x)=x^{2}, f(x)=x^{3},$ or $f(x)=|x|$ Then draw the graph of function $g$ using translations and/or a reflection. See Examples 7 and $8 .$ $$ g(x)=|x+4|+3 $$

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Key Concepts

Absolute Value Function

This function is the basic V-shaped graph defined by f(x) = |x|, where the vertex is at the origin and the graph is symmetric with respect to the y-axis. Its shape and structure serve as a foundation for understanding how other functions that involve absolute values can be manipulated through various transformations.

Graph Transformations

Graph transformations involve shifting, reflecting, stretching, or compressing a graph from its basic form. In this context, applying transformations to the absolute value function includes translating the graph horizontally and vertically. For example, in the function g(x) = |x+4|+3, the graph of |x| is shifted 4 units to the left and 3 units upward, illustrating how such modifications impact the position of the graph without altering its basic shape.

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