A student graphed f(x)=x and g(x)=f(x)+6 on the same coordinate grid. Which statement describes how the graphs of f and g are related?

Question

A student graphed f(x)=x and g(x)=f(x)+6 on the same coordinate grid. Which statement describes how the graphs of f and g are related?

Answer choices:

A. The graph of f is shifted 6 units up and made steeper to create g

B. The graph of f is less steeper than of g

C. The graph of f is shifted 6 units down and made steeper to create g

D. The graph of f is shifted 6 units up and the slope is the same as that of g

I'm struggling with this whole subject as a whole, so I would like someone to explain this subject in a summary for me. Other than that, I want to know the answer and how you knew that was the answer. Thank you!

Answer 1

Since g(x)=f(x)+6 we know this is a vertical shift upwards because for it to be a horizontal shift it would have to be g(x)=f(x+6), however since the 6 is outside of the parenthesis that means we are dealing with a vertical shift. Since the 6 is positive the vertical shift is upwards. We also know that g(x)=x+6 and the slope did not change, because we do not see f(x) being multiplied by a number which would cause a change in the slope. So therefore the answer must be D. If you have any questions feel free to ask at any time.