Question

Compare the functions f(x)=x and g(x)=14x. How are these graphs related?

a) They are parallel lines.
b) They intersect at the origin.
c) g(x) is a reflection of f(x) across the y-axis.
d) g(x) is a horizontal compression of f(x).

Answer 1

The functions f(x)=x and g(x)=14x both intersect at the origin, but because g(x) has a steeper slope than f(x), they are not parallel. The correct relationship between their graphs is that they intersect at the origin.

Step-by-step explanation:

The question involves comparing the functions f(x)=x and g(x)=14x to determine their relationship. By analyzing the given functions, we can see that both are linear equations of the general form y=mx+b, where m represents the slope and b the y-intercept. Both functions have a y-intercept of 0 since they are written without a constant term (b).

Function f(x)=x can be rewritten as y=1*x+0, which shows that it has a slope of 1. Similarly, function g(x)=14x can be rewritten as y=14*x+0, indicating a slope of 14. Since both functions have y-intercepts of 0, they intersect at the origin (0,0). However, because g(x) has a steeper slope than f(x), these lines are not parallel.

Therefore, the correct relationship between the graphs of f(x) and g(x) is that they intersect at the origin, making option b) the correct answer.

Answer 2

The functions f(x) = x and g(x) = 14x are linear functions. The graph of g(x) is a horizontal compression of the graph of f(x) with a steeper slope.

Step-by-step explanation:

The functions f(x) = x and g(x) = 14x are linear functions. The graph of f(x) is a straight line with a slope of 1, and the graph of g(x) is a straight line with a slope of 14.

The slope represents the rate of change of the y-values with respect to the x-values.

Since the slope of g(x) is greater than the slope of f(x), the graph of g(x) is steeper.

Therefore, the correct answer is d) g(x) is a horizontal compression of f(x).