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