a Apply the step to the parent function and compare the new function with g(x).
B
b Apply the step to the parent function and compare the new function with g(x).
C
c Compare the slopes of f(x) and g(x).
A
a Yes.
B
b Yes.
C
c No.
a Let's look at each of the given statements to decide if they describe a step in the transformation of f(x).
f(x)=x ⇒ g(x)=-1/3x-4First, we want to know if the transformation involves a reflection across the y-axis.
Let's graph the functions so that we can visualize what is happening to the function.
Notice that both functions, f(x) and g(x), are in slope-intercept form.
y= mx+ b
We will plot their y-intercepts and find a second point using the slope. Last, we will connect the points and draw the lines.
f(x)=x
g(x)=-1/3x-4
When we graph both functions, the slope changes from positive to negative. This indicates a reflection. Thus, the statement describes a step in this transformation.
b Now we want to know if the parent function is translated 4 units down. Let's look at the graphs once more.
f(x)=x
g(x)=-1/3x-4
Looking at both graphs, we can see that the y-intercept goes from 0 to -4. This indicates a translation down by 4 units. Therefore, the statement describes a step in this statement.
c Finally, we want to know if the parent function becomes more steep. The slope of the parent function, m=1, has an absolute value that is greater than the absolute value of the slope of g(x).
|1|>|-1/3|
Therefore, the parent function is more steep. When the transformation is applied, the function becomes less steep. which means that the statement does not describes a step in this transformation.
