The graph of function g is transformed to create the graph of function h.
g(x)=x
h(x)=¼g(x)-12
Which statement about the relationships of these two graphs is true?
The graph of function g is transformed to create the graph of function h.
g(x)=x
h(x)=¼g(x)-12
Which statement about the relationships of these two graphs is true?
The graph of h(x) is less steep than g(x) and the y-intercept has been translated up.
The graph of h(x) is less steep than g(x) and the y-intercept has been translated down.
The graph of h(x) is steeper than g(x) and the y-intercept has been translated down.
The graph of h(x) is steeper than g(x) and the y-intercept has been translated up
To determine the relationships between the graphs of the function g(x)=x and h(x)=¼g(x)-12, we must analyze the transformation applied to g(x) to obtain h(x).
The function h(x) is defined in terms of g(x) as follows:
h(x) = ¼g(x) - 12
= ¼x - 12
There are two main transformations here:
1. Vertical scaling by a factor of ¼: Multiplying the function g(x) by ¼ makes the slope of the graph of h(x) less steep than the graph of g(x). Since the original function g(x) has a slope of 1 (the coefficient of x), multiplying it by ¼ gives h(x) a slope of ¼, which is less steep than a slope of 1.
2. Vertical translation down by 12 units: Subtracting 12 from the function g(x) translates the graph of h(x) 12 units down along the y-axis.
Given these transformations, we can deduce the correct statement about the relationship between the graphs of functions g and h:
"The graph of h(x) is less steep than g(x) and the y-intercept has been translated down."
Therefore, the second statement you provided is the correct one:
The graph of h(x) is less steep than g(x) and the y-intercept has been translated down.