Answer:
The first option "g(x) is the graph of f(x) = log x shifted 2 units to the left and is compressed vertically by a factor of [tex]\frac{1}{2}[/tex] " is the right answer.
Step-by-step explanation:
Let us consider the function f(x) = log x. Lets add a constant c to the input of parent function i.e f(x) = log x. It would produce a horizontal translation, to the left by c units.
If c > 0, it shifts the function f(x) = log x to the left c units.
If c < 0, it shifts the function f(x) = log x to the right c units.
As c > 0,
Hence, the function f(x) = log x shifts to the left c units
Also,
if f(x) = log x is multiplied by a constant c > 0, the result is a vertical stretch or compression of the original graph.
if c > 0, it stretches the function f(x) = log x vertically by a factor of c.
if 0 < c < 1, it compresses the function f(x) = log x vertically by a factor of c.
As 0 < c < 1,
Hence, it compresses the function f(x) = log x vertically by a factor of c.
So, the first option "g(x) is the graph of f(x) = log x shifted 2 units to the left and is compressed vertically by a factor of [tex]\frac{1}{2}[/tex] " is the right answer.
Keywords: transformation, function
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