Answer:
See the attached for a graph with labeled intercepts. (You will have to round the numbers.)
Step-by-step explanation:
The graph of 1.5^x is reflected across the x-axis, then translated 2 units to the right and 4 units up.
A graphing calculator can be a great help for graphing or figuring the intercepts. The y-intercept will be f(0) = -1/2.25 +4 ≈ 3.56.
The x-intercept will be at the x-value where ...
-1.5^(x-2) +4 = 0
4 = 1.5^(x -2) . . . . add 1.5^(x-2)
log(4) = (x -2)·log(1.5) . . . . take the logarithm
log(4)/log(1.5) = x -2 . . . . . divide by log(1.5)
2 + log(4)/log(1.5) = x ≈ 5.42
_____
Your calculator or a spreadsheet can help evaluate the function for various values of x. The second attachment shows the calculations done by a spreadsheet program. Note that the minus sign needs special treatment because the spreadsheet does not strictly follow the order of operations.
You can even use a spreadsheet's "Goal Seek" function to find the y-intercept. Have it adjust the x-value until the y-value is zero.
