Answer :
The equation for the function which would have the given graph is:
f(x) = { 2x - 8, for -12 ≤ x ≤ -2}, { 0.5x + 6, for -2 < x ≤ 6}, {-2x + 10, for 6 < x ≤ 12}.
The given graph is shown below:
The graph shows that the function has three separate line segments which means the function may have different equations for different intervals.
Therefore, we can determine the function equation using each line segment.
First interval: The interval is from -12 to -2 with a slope of 2 and y-intercept -8. f(x) = 2x - 8.
Second interval: The interval is from -2 to 6 with a slope of 0.5 and y-intercept 6. f(x) = 0.5x + 6.
Third interval: The interval is from 6 to 12 with a slope of -2 and y-intercept 10. f(x) = -2x + 10.
Thus, the equation for the function which would have the given graph is:
f(x) = { 2x - 8, for -12 ≤ x ≤ -2}, { 0.5x + 6, for -2 < x ≤ 6}, {-2x + 10, for 6 < x ≤ 12}.
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