If the function \(g(x) = x^2 - 4\), what are the x-intercepts of the function?

If the function \(g(x) = x^2 - 4\), what are the x-intercepts of the function?

• A. 4 and -4
• B. 2 and -2
• C. -4 and 0
• D. 0 and 4

Answer: (A)

To find the x-intercepts of the function \(g(x) = x^2 - 4\), we need to determine the values of \(x\) for which \(g(x) = 0\). This means we will set the function equal to zero and solve for \(x\): \[ x^2 - 4 = 0 \] Next, we can factor the left-hand side of the equation: \[ (x - 2)(x + 2) = 0 \] Now, we can apply the zero product property, which tells us that if the product of two factors equals zero, then at least one of the factors must be zero. This leads to two equations: 1. \(x - 2 = 0\), so \(x = 2\) 2. \(x + 2 = 0\), so \(x = -2\) Therefore, the x-intercepts of the function occur at \(x = 2\) and \(x = -2\). This is why the correct answer consists of the values 2 and -2, where the function crosses the x-axis. This clarification in the context of intercepts helps to reinforce understanding of

To find the x-intercepts of the function (g(x) = x^2 - 4), we need to determine the values of (x) for which (g(x) = 0). This means we will set the function equal to zero and solve for (x):

[

x^2 - 4 = 0

]

Next, we can factor the left-hand side of the equation:

[

(x - 2)(x + 2) = 0

]

Now, we can apply the zero product property, which tells us that if the product of two factors equals zero, then at least one of the factors must be zero. This leads to two equations:

1. (x - 2 = 0), so (x = 2)

2. (x + 2 = 0), so (x = -2)

Therefore, the x-intercepts of the function occur at (x = 2) and (x = -2).

This is why the correct answer consists of the values 2 and -2, where the function crosses the x-axis. This clarification in the context of intercepts helps to reinforce understanding of