Question

Find g(x), where g(x) is the translation 4 units right and 10 units up of f(x)=x.
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:
\[
g(x) = x + 6.
\]