Find g(x), where g(x) is the translation 4 units right and 10 units up of f(x)=x.

Question

Write your answer in the form mx+b, where m and b are integers.
g(x)=

Answer 1

To find the translated function \( g(x) \) from the original function \( f(x) = x \), we need to apply the given translations: 4 units to the right and 10 units up.

1. Translation 4 units to the right: To translate a function \( f(x) \) to the right by \( h \) units, we replace \( x \) with \( x-h \). In this case, \( h = 4 \), so we have: \[ f(x-4) = x - 4. \]

2. Translation 10 units up: To move a function up by \( k \) units, we add \( k \) to the function. Here, \( k = 10 \). Therefore: \[ g(x) = f(x-4) + 10 = (x - 4) + 10. \]

3. Simplify the expression: \[ g(x) = x - 4 + 10 = x + 6. \]

Thus, in the form \( mx + b \), we have:

• \( m = 1 \)
• \( b = 6 \)

The final answer is: \[ g(x) = x + 6. \]