The graph of the function f(x) is shown. Which is the value of f(-1)?
On a coordinate plane, a line labeled F of X has a positive slope, passes through (negative 3, negative 12), crosses the Y-axis at (0, negative 7 point 5), further extends to cross the X-axis at (5, 0), and end at (13, 12).
CLEAR SUBMIT
−9
−6
413
523
From the given information, we can see that the line labeled F of X passes through (-3, -12) and (5, 0). Therefore, the slope of the line can be calculated as:
slope = (change in y-coordinate)/(change in x-coordinate)
slope = (-12-0)/(-3-5) = -12/-8 = 3/2
Using the slope-intercept form of a linear equation, we can find the equation of the line as:
y = mx + b, where m is the slope and b is the y-intercept
Using the point (0, -7.5) on the line, we can solve for b:
-7.5 = (3/2)(0) + b
-7.5 = b
So, the equation of the line is:
y = (3/2)x - 7.5
To find f(-1), we can substitute x = -1 into the equation:
f(-1) = (3/2)(-1) - 7.5
f(-1) = -3/2 - 7.5
f(-1) = -3/2 - 15/2
f(-1) = -18/2
f(-1) = -9
Therefore, the value of f(-1) is -9. Answer: -9.