Question

what is the range of f? choose 1 answer: a $-3 leq f(x) leq 7$ b the $f(x)$-values $-3, 3, 6,$ and $7$ c $-6 leq f(x) leq 6$ d the $f(x)$-values $-6, -4, -2,$ and $6$

Explanation:

Step1: Understand the range of a function

The range of a function is the set of all possible output values (y - values) the function can take. For a graph, we look at the minimum and maximum y - values it reaches.

Step2: Analyze the graph

Looking at the given graph of the function \(f\):

• The lowest point (minimum y - value) on the graph has a \(y\) - coordinate of \(- 3\).
• The highest point (maximum y - value) on the graph has a \(y\) - coordinate of \(7\).

So the range of the function \(f\) is all the \(y\) - values (or \(f(x)\) values) from \(-3\) up to \(7\), which can be written as \(-3\leq f(x)\leq7\).

Let's check the other options:

• Option B: The function is a piece - wise linear function, not just taking the values \(-3,3,6,7\). It takes all values between \(-3\) and \(7\) as well.
• Option C: The minimum value is \(-3\) not \(-6\) and the maximum is \(7\) not \(6\).
• Option D: The function does not take the values \(-6,-4,-2\) as its output.

Answer:

A. \(-3\leq f(x)\leq7\)