Question

Compare the functions f(x) = x5 and g(x) = 5x by graphing both functions in several viewing rectangles. find all points of intersection of the graphs correct to one decimal place. (enter your answers as a comma-separated list. round any decimal answers to one decimal place.)

Answer 1

To compare the functions f(x) = x^5 and g(x) = 5x, graph both functions and find their points of intersection.

Step-by-step explanation:

To compare the functions f(x) = x^5 and g(x) = 5x, we can graph both functions in several viewing rectangles. By finding the points of intersection of the graphs, we can compare their values at those points.

1. Start by graphing the function f(x) = x^5 using a graphing calculator or software. This will give us a curve with a steep increase as x gets larger.
2. Next, graph the function g(x) = 5x in the same viewing rectangle as f(x). This will give us a straight line that increases more gradually as x gets larger.
3. Identify the points of intersection between the graphs of f(x) and g(x). These are the x-values at which the two functions have the same y-value. Round these x-values to one decimal place and list them as the points of intersection.

Answer 2

The graphs of
f(x) = x⁵ and g(x) = 5x
are shown in the figure below.
The initial plot interval is -2 ≤ x ≤ 2.

In order to determine the points of intersection (to 1 decimal place accuracy) more graphs (shown in accompanying figures) were necessary.
The points of intersection are
x = -1.5, x = 0, and x = 1.5

Answer:
The points of intersection are x = -1.5, 0, and 1.5 (accurate to 1 decimal place)