Problem 110 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

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 1 - 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.

Step 2 - Substitute the value of x = -3

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

Step 3 - Substitute the value of x = -2

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

Step 4 - Substitute the value of x = -1

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

Step 5 - Substitute the value of x = 0

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

Step 6 - Substitute the value of x = 1

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

Step 7 - Substitute the value of x = 2

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

Step 8 - Substitute the value of x = 3

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