Use a graphing calculator to graph the original function y=12x−4

Question

and the vertically dilated function with a factor k=6
. Determine the x-intercepts of both functions.(1 point)
Responses

The original function has an x-intercept of (−8,0)
, and the dilated function has an x-intercept of (−8,0)
.
The original function has an x -intercept of left parenthesis negative 8 comma 0 right parenthesis , and the dilated function has an x -intercept of left parenthesis negative 8 comma 0 right parenthesis .

The original function has an x-intercept of (8,0)
, and the dilated function has an x-intercept of (48,0)
.
The original function has an x -intercept of left parenthesis 8 comma 0 right parenthesis , and the dilated function has an x -intercept of left parenthesis 48 comma 0 right parenthesis .

The original function has an x-intercept of (8,0)
, and the dilated function has an x-intercept of (8,0)
.
The original function has an x -intercept of left parenthesis 8 comma 0 right parenthesis , and the dilated function has an x -intercept of left parenthesis 8 comma 0 right parenthesis .

The original function has an x-intercept of (0,−4)
, and the dilated function has an x-intercept of (0,−24)
.

Answer 1

To find the x-intercepts of both the original function $y=12x-4$ and the vertically dilated function with a factor $k=6$, we can break the steps down as follows:

1. Finding the x-intercept of the original function

The x-intercept occurs where $y=0$. For the original function: $$0=12x-4$$ Adding 4 to both sides: $$4=12x$$ Dividing both sides by 12: $$x=\frac{4}{12}=\frac{1}{3}$$

Thus, the x-intercept of the original function is: $$(\frac{1}{3},0)$$

2. Finding the x-intercept of the vertically dilated function

The vertically dilated function with a factor of $k=6$ is: $$y=6(12x-4)=72x-24$$ To find the x-intercept for this function: $$0=72x-24$$ Adding 24 to both sides: $$24=72x$$ Dividing both sides by 72: $$x=\frac{24}{72}=\frac{1}{3}$$

Thus, the x-intercept of the dilated function is: $$(\frac{1}{3},0)$$

Conclusion

After calculating, we find that:

• The original function $y=12x-4$ has an x-intercept of $(\frac{1}{3},0)$
• The vertically dilated function $y=72x-24$ also has an x-intercept of $(\frac{1}{3},0)$

None of the responses provided match the correct x-intercept calculations.