Question
How would \( y-x^{2}=5 \) be written in function notation?
Ask by Martinez Parsons. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( y = x^{2} + 5 \) can be written as \( f(x) = x^{2} + 5 \).
Solution
To express the equation \( y - x^{2} = 5 \) in function notation, we need to solve for \( y \) in terms of \( x \).
1. Start with the original equation:
\[
y - x^{2} = 5
\]
2. Add \( x^{2} \) to both sides to isolate \( y \):
\[
y = x^{2} + 5
\]
Now, we can express this in function notation. We typically denote a function as \( f(x) \). Therefore, we can write:
\[
f(x) = x^{2} + 5
\]
This means that the function \( f \) takes an input \( x \) and outputs \( x^{2} + 5 \).
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Simplify this solution Mind Expander
To write the equation \( y - x^{2} = 5 \) in function notation, we simply solve for \( y \). This gives us \( y = x^{2} + 5 \). Therefore, we can express this as \( f(x) = x^{2} + 5 \), where \( f(x) \) denotes the function output corresponding to the input \( x \). In function notation, we emphasize the relationship between the input and output. So whenever you input a specific value of \( x \) into \( f(x) \), you’ll always get the corresponding \( y \) value as \( y = x^{2} + 5 \). It's like a magical rule that always works, making math a bit more fun!
