Question

Choose the graph which matches the function. (2 points)
f(x) = 3x-4

Answer 1

The last image is the graph of
`y = 3^x`

In fact, it is an increasing exponential function, and it passes through the points
`(0,1)`, which reflects the fact that
`3^0=1` and
`(1,3)`, which reflects the fact that
`3^1=3`.

Now,
`y = 3^(x-4)` is a child of the parent function we just described. Precisely, it is the result of the transformation
`f(x) \to f(x-4)`

In general, every time you perform a transformation like
`f(x) \to f(x+k)`, you translate the graph horizontall, k units to the left if k is positive, and k units to the right if k in negative.

Since in this case
`k = - 4`, we have a horizontal translation of 4 units to the right.

So, the correct option is the third one, because:

• The first graph is the parent function translated 4 units to the left
• The second graph is the parent function translated 4 units down
• The third graph is the parent function translated 4 units to the right
• The fourth graph is the parent function