QuestionAnalyze the graph of $f$ to find intersections with $y=1$ , $x=5$ , and solve $f(x)=-6$ . Use given points for help.

Studdy Solution

STEP 1

Assumptions1. The points given are all points on the graph of the function $f$ . . The line $y=1$ and $x=5$ are straight lines.
3. The function $f$ is continuous and smooth between the given points.

STEP 2

To determine how often the line $y=1$ intersects the graph, we need to find the number of points where the $y$ -coordinate is $1$ . Since none of the given points have a $y$ -coordinate of $1$ , we can conclude that the line $y=1$ does not intersect the graph.

STEP 3

To determine how often the line $x=5$ intersects the graph, we need to find the number of points where the $x$ -coordinate is $5$ . Since none of the given points have an $x$ -coordinate of $5$ , we can conclude that the line $x=5$ does not intersect the graph.

STEP 4

To find the value(s) of $x$ for which $f(x)=-6$ , we need to find the $x$ -coordinates of the points where the $y$ -coordinate is $-6$ . From the given points, we see that $f(x)=-6$ at $x=4$ and $x=-14$ .
So, the answers to the questions are(k) The line $y=1$ intersects the graph0 times. (l) The line $x=$ intersects the graph0 times. (m) The values of $x$ for which $f(x)=-6$ are $x=4$ and $x=-14$ .

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