Question

what is the range of ( f )?
choose 1 answer:
a ( -9 leq f(x) leq -2 )
b ( -9 leq f(x) leq 9 )
c ( -8 leq f(x) leq -4 )
d ( -2 leq f(x) leq 9 )

Explanation:

Step1: Identify the minimum and maximum y - values

To find the range of a function from its graph, we need to determine the minimum and maximum values of the \(y\) - coordinate (the value of \(f(x)\)) that the graph attains.

Looking at the graph, we observe the highest point (maximum \(y\) - value) and the lowest point (minimum \(y\) - value) of the function's graph.

From the graph, the maximum value of \(f(x)\) (the highest \(y\) - coordinate) is \(9\) (since the graph reaches up to \(y = 9\)) and the minimum value of \(f(x)\) (the lowest \(y\) - coordinate) is \(- 9\) (since the graph goes down to \(y=-9\)).

Step2: Determine the range

The range of a function \(y = f(x)\) is the set of all possible \(y\) - values (outputs) of the function. If the minimum value of \(f(x)\) is \(m\) and the maximum value is \(M\), then the range is \(m\leq f(x)\leq M\).

Here, \(m=-9\) and \(M = 9\), so the range of the function \(f\) is \(-9\leq f(x)\leq9\).

Answer:

B. \(-9\leq f(x)\leq9\)