Questions: Find (g(x)), where (g(x)) is the translation 4 units up of (f(x)=10 x-7). Write your answer in the form (m x+b), where (m) and (b) are integers.

Transcript text: Find $g(x)$, where $g(x)$ is the translation 4 units up of $f(x)=10 x-7$. Write your answer in the form $m x+b$, where $m$ and $b$ are integers. \[ g(x)= \]

Solution

Solution Steps

Step 1: Identify the original function

The original function is given as $ f(x) = 10x - 7 $.

Step 2: Understand the transformation

The function $ g(x) $ is a translation of $ f(x) $ 4 units up. Translating a function up by $ k $ units involves adding $ k $ to the original function.

Step 3: Apply the transformation

To translate $ f(x) $ 4 units up, add 4 to $ f(x) $: \[ g(x) = f(x) + 4 = (10x - 7) + 4 \]

Step 4: Simplify the expression

Combine like terms: \[ g(x) = 10x - 7 + 4 = 10x - 3 \]