Question

use the graph of ( y = f(x) ) to answer the questions. complete parts a through j
neither
h. for what values of ( x ) is ( f(x)>0 )?
the set of ( x )-values for which ( f(x)>0 ) is ( (-infty,-1) cup(1, infty) )
(type your answer in interval notation)
i. determine whether ( f(4)>f(-1) ) is true or false. choose the correct
answer below.
a. false, because the ( y )-value where ( x = 4 ) is greater than
the ( y )-value where ( x=-1 )
b. true, because the ( y )-value where ( x = 4 ) is less than the ( y )-value
where ( x=-1 )
c. true, because the ( y )-value where ( x = 4 ) is greater than the ( y )-value
where ( x=-1 )
d. false, because the ( y )-value where ( x = 4 ) is less than the ( y )-value
where ( x=-1 )
j. for what value(s) of ( x ) is ( f(x)=5 )?
the set of ( x )-values for which ( f(x)=5 ) is
(type your answer in interval notation)

Explanation:

Step1: Locate \(x = 4\) and \(x=-1\) on the graph

For \(x = 4\), the \(y -\)value \(f(4)=5\). For \(x=-1\), from the graph, we can see that the \(y -\)value \(f(-1)\) is not given directly. But we know that when \(x=-4\), \(y = 5\) and the function's behavior. Since \(f(4)=5\) and \(f(-1)\) is not \(5\) (from the graph's structure, \(f(-1)\) is not at the same height as \(f(4)\)). In fact, \(f(4)\) is greater than \(f(-1)\) as \(f(4)\) is at a higher point on the \(y -\)axis.

Step2: Analyze the equation \(f(x)=5\)

We look for the \(x -\)values where the \(y -\)value (i.e., \(f(x)\)) is equal to \(5\). From the graph, when \(y = 5\), \(x=-4\) and \(x = 4\)

Answer:

i. C. True, because the \(y -\)value where \(x = 4\) is greater than the \(y -\)value where \(x=-1\)
j. The set of \(x -\)values for which \(f(x)=5\) is \(\{-4,4\}\)