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Chapter 0: Problem 110

Will help you prepare for the material covered in the first section of the next chapter. If \(y=4-x^{2},\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with \(-3\) and ending with 3

Short Answer

Expert verified
The corresponding \(y\) values for each integer value of \(x\) from -3 to 3 are -5, 0, 3, 4, 3, 0, and -5 respectively.

Step by step solution

01

- Identify the function and the range of x values

The function given is \(y = 4 - x^2\). We need to find the corresponding y values for each integer value of x starting from -3 and ending with 3.
02

- Substitute the value of x = -3

When \(x = -3\), substituting x into the function, we get \(y = 4 - (-3)^2 = 4 - 9 = -5\)
03

- Substitute the value of x = -2

When \(x = -2\), substituting x into the function, we get \(y = 4 - (-2)^2 = 4 - 4 = 0\)
04

- Substitute the value of x = -1

When \(x = -1\), substituting x into the function, we get \(y = 4 - (-1)^2 = 4 - 1 = 3\)
05

- Substitute the value of x = 0

When \(x = 0\), substituting x into the function, we get \(y = 4 - 0^2 = 4 - 0 = 4\)
06

- Substitute the value of x = 1

When \(x = 1\), substituting x into the function, we get \(y = 4 - 1^2 = 4 - 1 = 3\)
07

- Substitute the value of x = 2

When \(x = 2\), substituting x into the function, we get \(y = 4 - 2^2 = 4 - 4 = 0\)
08

- Substitute the value of x = 3

When \(x = 3\), substituting x into the function, we get \(y = 4 - 3^2 = 4 - 9 = -5\)

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