Question

The graph of f(x)=(1/4)3^x-6 is shown below. g(x) is a transformation of f(x). How would you write the equation for the function g(x)?

http://media.apexlearning.com/Images/201308/27/bedf8005-5d2d-42cc-bc09-82867f7fe4f4.jpg

A. g(x)=(1/4)3^x + 2
B. g(x)=3^x + 2
C. g(x)=(1/3) • 4^x + 3
D. g(x)=(-1/4)3^x - 6

Any help and an explanation would be great! The +/- at the end of the equations are separate from the exponents.

Answer 1

The link doesn't work btw, it says we dont have permission
Try attaching a screenshot?

Answer 2

That would explain the lack of responses. Thanks! Here's a screenshot.

Answer 3

The only thing that is different about g(x) is that it has a vertical shift of about 9 (moved up 9)
Each number in graphing form of an equation manipulates a graph in a different way, for example in the equation y=a(x-b)^c + d

a changes how vertically stretched the graph is (>1 stretches it, <1 squishes it)
b shifts it horizontally (positive to the right, negative to the left)
c (what power the x is raised to) completely changes the shape of the graph (x^1 is a line, x^2 a parabola, x^3 is a wavy cubic function... etc) and also tells you how many times it crosses the x axis
d gives you your vertical shift, this is what you're looking for

The only equation that looks almost identical but has a different +something on the end would be A, that's your answer

Answer 4

Btw, those are all called function or graph transformations, there are tons of great google images that demonstrate each

Also, if you're allowed calculators on homework and tests, that's a great problem to just graph each of those on your calculator and see from there. If you ever find yourself stuck like "oh what does it mean when the x is multiplied by a fraction" you can always just make up an equation and graph it along with the original function and see what the difference is

Answer 5

Thanks for the explanation. I'm taking this stuff online and it's complicated for the sake of being complicated. Thanks for spelling it out for me. It really clarifies the lesson for me.

Unfortunately I can only use a graphing calculator when I go to the class to take these tests.