how does the graph of the transformed function g(x)=log_5(4x-16) compare to the graph of its parent function f(x)=log_5x
a. The transformed function has been compressed horizontally and translated 16 units to the right.
b.The transformed function has been stretched horizontally and translated 16 units to the right.
c. The transformed function has been compressed horizontally and translated 4 units to the right.
d. The transformed function has been stretched horizontally and translated 4 units to the right.
c. The transformed function has been compressed horizontally and translated 4 units to the right.
Apologies for the confusion, but that is not the correct answer. The correct answer is b. The transformed function has been stretched horizontally and translated 16 units to the right.
the correct answer is c. The transformed function has been compressed horizontally and translated 4 units to the right.
I apologize for the earlier incorrect response. You are correct. The correct answer is c. The transformed function g(x) = log_5(4x-16) has been compressed horizontally by a factor of 4 and translated 4 units to the right compared to its parent function f(x) = log_5x. Thank you for pointing out the mistake.
explain why the answer is c. The transformed function has been compressed horizontally and translated 4 units to the right.
Apologies for the confusion caused by my previous response. Thank you for pointing out the error.
To analyze the transformation, let's consider the given function g(x) = log_5(4x-16) and its parent function f(x) = log_5x.
First, let's look at the inside of the logarithm function, which is (4x - 16). To compress or stretch a function horizontally, we look at the coefficient of x. In this case, the coefficient of x is 4, which means there is a horizontal compression by a factor of 4.
Next, let's consider the constant term inside the logarithm function, which is -16. A positive constant value inside the logarithm function causes a horizontal translation to the right by that value. In this case, we have a constant term of -16, so the graph is translated 16 units to the right.
Therefore, the transformed function g(x) = log_5(4x - 16) has been compressed horizontally by a factor of 4 (or compressed horizontally) and translated to the right by 16 units.
Therefore, the correct answer is c. The transformed function has been compressed horizontally and translated 4 units to the right.
The correct answer is b. The transformed function has been stretched horizontally and translated 16 units to the right.
To see this, let's analyze the transformation. In the transformed function g(x) = log_5(4x-16), we have a horizontal compression factor of 1/4 (since the coefficient of x is 4 instead of 1) and a horizontal shift of 16 units to the right (since there is a -16 in the inside of the logarithm function).
On the other hand, the parent function f(x) = log_5x has no horizontal compression or stretching (since the coefficient of x is 1) and no horizontal shift (since there is no constant term inside the logarithm function).
Therefore, the graph of g(x) = log_5(4x-16) will be a horizontally stretched version of the graph of f(x) = log_5x, shifted 16 units to the right.