Question
The function \( f \) is defined as follows. \( f(x)=3 x^{2}-8 \) If the graph of \( f \) is translated vertically upward by 5 units, it becomes the graph of a Find the expression for \( g(x) \). Note that the ALEKS graphing calculator may be helpful in checking your answer. \( g(x)=\square \)
Ask by Lambert Marshall. in the United States
Feb 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( g(x) = 3x² - 3 \)
Solution
Translating f(x) = 3x² – 8 vertically upward by 5 units means you add 5 to the entire function.
Thus, g(x) = f(x) + 5
= (3x² – 8) + 5
= 3x² – 3
So, the expression for g(x) is 3x² – 3.
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Simplify this solution Mind Expander
To find the expression for \( g(x) \), we need to take the original function \( f(x) = 3x^2 - 8 \) and translate it vertically upward by 5 units. This means we will add 5 to the entire function: \[ g(x) = f(x) + 5 = (3x^2 - 8) + 5 \] Simplifying this gives: \[ g(x) = 3x^2 - 3 \] So, the expression for \( g(x) \) is \( 3x^2 - 3 \).
