Question

selected values of functions \\(c(x)\\) and \\(d(x)\\) are given in the table.

\\(\

$$\begin{array}{|c|c|c|c|c|c|c|}\\hline x & -3 & -2 & -1 & 0 & 1 & 2 \\\\\\hline c(x) & 4 & 0 & -4 & -8 & -4 & 0 \\\\\\hline d(x) & -1 & -2 & -4 & -8 & -16 & -32 \\\\\\hline\\end{array}$$

\\)

which key feature do the functions have in common?

an x-intercept at \\((0, -8)\\)

an x-intercept at \\((-2, 0)\\)

a y-intercept at \\((0, -8)\\)

Explanation:

Analyze the given table

We examine the values of \(c(x)\) and \(d(x)\) at each given \(x\):

• At \(x = 0\), we have \(c(0) = -8\) and \(d(0) = -8\).

Define intercepts

An \(x\)-intercept occurs where the function value is \(0\), written as \((x, 0)\).
A \(y\)-intercept occurs where \(x = 0\), written as \((0, y)\).

Evaluate the options

• "An x-intercept at (0, -8)": Incorrect, because \(y

eq 0\).

• "An x-intercept at (-2, 0)": Incorrect, because \(d(-2) = -2

eq 0\).

• "A y-intercept at (0, -8)": Correct, since both functions have \(y = -8\) when \(x = 0\).

Answer:

• An x-intercept at (0, -8)
• An x-intercept at (-2, 0)
• A y-intercept at (0, -8) (Correct answer)