Question

2. (a. Two power functions are given. Simplify both functions.

f(x) = 5x³.x²
g(x) = (2x)S
(b) Which function grows faster? Explain how you know.
11/1
Both power functions from part a are graphed to the right. Label
each function on the graph. Explain how you know which is which.
19

Answer 1

Part a:

f(x) = 5x^3 * x^2 = 5x^5

g(x) = (2x)^8 = 2^8 * x^8 = 256x^8

Part b: Function g(x) grows faster. This is because it has a higher exponent (8 vs 5). The higher the exponent, the faster a power function grows.

Part c: Graph explanation:

The steeper curve is g(x) because it has the higher exponent. As a power function's exponent increases, its slope gets steeper.

Therefore, the gentler curve is f(x), which has the lower exponent of 5.

So in summary:

a) The simplified power functions are:

f(x) = 5x^5

g(x) = 256x^8

b) Function g(x) grows faster due to its higher exponent of 8 compared to f(x)'s exponent of 5.

c) On the graph:

The steeper curve is g(x), which has the higher exponent.

The gentler curve is f(x), which has the lower exponent.

Hope this explanation makes sense! Let me know if you have any other questions.