Graph the function. Compare the graph to the graph of the parent function. Describe the domain and range of f.

Question

f (x) = −2(4)x and f (x) = 2 ( 1/4 )x

Answer 1

For both f(x) = -2(4)x and f(x) = 2 (1/4 )x , the parent function is going to be f(x) = x, which is a simple linear function with a slope of 1 that passes through the origin (0,0) from the third quadrant to the first quadrant and extends forever.

Let's start by simplifying the two functions:

f(x) = -2(4)x is the same as f(x) = -8x when you simplify using the laws of distribution.

f(x) = 2 (1/4 )x would then become f(x) = (2/4)x which could be further simplified to f(x) = (1/2)x

To compare f(x) = -8x to the parent function of f(x) = x, we automatically know that the function when graphed will be a negative slope that passes through the origin from the second quadrant to the fourth quadrant, but it will be 8 times as steep as the parent function. This is easiest to view if entered onto a graphing calculator or by simply typing the function into Google.

To compare f(x) = (1/2)x to the parent function of f(x) = x, we know that the function will be positive but it will only be half as steep as the parent function. This is easiest to view if entered onto a graphing calculator or by simply typing the function into Google.

Finally, the domain and range of both of the above functions will be all real numbers, or R. This is because both functions will cross every x and y value at some point.

I hope this was helpful!