or
Find g(x), where g(x) is the translation 8 units up of f(x)=|x|.
Write your answer in the form a|x–h|+k, where a, h, and k are integers.
g(x)=

To find the function \( g(x) \) that represents the translation of \( f(x) = |x| \) 8 units up, we modify the equation by adding 8 to the output of the function.

The original function is:

\[
f(x) = |x|
\]

When translating a function upward by \( k \) units, we add \( k \) to the function:

\[
g(x) = f(x) + 8 = |x| + 8
\]

Now, the given form is \( a|x - h| + k \). In this case:

- \( a = 1 \) (since the slope of the absolute value is unchanged),
- \( h = 0 \) (there's no horizontal shift),
- \( k = 8 \) (the vertical translation).

Thus, the function becomes:

\[
g(x) = 1|x - 0| + 8
\]

Simplified:

\[
g(x) = |x| + 8
\]

Would you like further details or have any questions?

Here are 5 related questions for you:
1. How would the equation change if we translated \( f(x) = |x| \) 5 units down instead?
2. What happens to the graph of \( f(x) = |x| \) when translated 3 units to the right?
3. How do you find the horizontal translation of \( f(x) = |x| \)?
4. If \( f(x) = 2|x| \), what is the translation 8 units up?
5. What are the effects of translating a function both horizontally and vertically?

**Tip:** Vertical translations simply add or subtract from the function's output, while horizontal translations affect the input inside the function.

Find g(x), where g(x) is the translation 8 units up of f(x) = |x|. Write your answer in the form a|x–h|+k, where a, h, and k are integers.

Discover how to translate the absolute value function f(x) = |x| by 8 units up. This tutorial explains the translation process using key algebraic concepts and formulas, ideal for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation