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vovangra [49]
3 years ago
9

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

Mathematics
1 answer:
vovangra [49]3 years ago
5 0

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
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