We have a function for which we only have the chart.
We need to find the value of x so that f(x)=7.
NOTE: As we are lookin for the value of x that makes the value of f(x) = 7, we are able to see it in the graph directly:
If we start at y=7, we can draw a line until we intersect the line for f(x). When this happens we draw a vertical line towards the x-axis until we intersect it.
The value of x at that point is the one that makes f(x)=7.
If we can not find the solution by graph, we have to find the equation of the line and clear x for f(x)=7.
SOLUTION WITH EQUATION:
With the information from the chart we have to find the equation.
We can identify two points in the function: (2,0) and (5,7).
Using the 2 known points, we calculate the slope of the line as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{7-0}{5-2}=\frac{7}{3}[/tex]
Then, we can write the slope-point equation as:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-0=\frac{7}{3}(x-2) \\ y=\frac{7}{3}x-\frac{14}{3} \end{gathered}[/tex]
Then, if we know that y=7, we can replace y with this value and calculate x as:
[tex]\begin{gathered} y=7=\frac{7}{3}x-\frac{14}{3} \\ 7\cdot3=7x-14 \\ 21=7x-14 \\ 7x=21+14 \\ 7x=35 \\ x=\frac{35}{7} \\ x=5 \end{gathered}[/tex]
Answer: the value of x so that f(x)=7 is x=5.
