Jennifer started with $50 in her savings account. Each week she withdrew $10. The amount of money in her savings account after x weeks is represented by the function f(x) = 50 - 10x. Find the intercepts.
To find the intercepts of the function f(x) = 50 - 10x, we need to determine the points where the graph of the function crosses the x-axis (x-intercept) and the y-axis (y-intercept).
1. X-intercept: The x-intercept is the point where the graph intersects the x-axis, meaning the value of y is zero. To find it, we set f(x) = 0 and solve for x:
50 - 10x = 0
Subtract 50 from both sides:
-10x = -50
Divide both sides by -10:
x = 5
Therefore, the x-intercept is at (5, 0).
2. Y-intercept: The y-intercept is the point where the graph intersects the y-axis, meaning the value of x is zero. To find it, we substitute x = 0 into the function:
f(0) = 50 - 10(0)
f(0) = 50 - 0
f(0) = 50
Therefore, the y-intercept is at (0, 50).
In summary, the intercepts of the function f(x) = 50 - 10x are (5, 0) for the x-intercept and (0, 50) for the y-intercept.
y=50-10x
set y=0 to find the x-intercept
set x=0 to find the y-intercept.