Compare the given linear function to its parent function f(x) and determine the transformations:
g(x) = -1/3f(x) + 5
The new function is (1) and (2) and (3)
(1).
A. Reflected over the x-axis
B. did not reflect over the x-axis
(2)
A. steeper than the parent function
B. less steep than the parent function
(3)
A. shifted up 5 units
B. shifted down 5 units
C. no vertical shift
The given linear function is g(x) = -1/3f(x) + 5.
(1) The new function is reflected over the x-axis because of the negative coefficient (-1/3) multiplying f(x). Therefore, the answer is A. Reflected over the x-axis.
(2) The new function is less steep than the parent function because of the absolute value of the fraction in front of f(x), which is 1/3. Since 1/3 is less than 1, the new function is less steep. Therefore, the answer is B. Less steep than the parent function.
(3) The new function is shifted up 5 units because of the constant term added at the end, which is +5. Therefore, the answer is A. Shifted up 5 units.
To compare the given linear function g(x) = -1/3f(x) + 5 to its parent function f(x), let's analyze each transformation step-by-step.
(1) Reflection over the x-axis:
The given function g(x) = -1/3f(x) + 5 does not include a reflection over the x-axis since there is no negative sign in front of the parent function f(x).
Answer: (1) B. did not reflect over the x-axis
(2) Steeper/less steep than the parent function:
The coefficient in front of f(x) in the given function is -1/3. Since the absolute value of this coefficient is less than 1, the function is less steep than the parent function f(x).
Answer: (2) B. less steep than the parent function
(3) Vertical shift:
In the given function g(x) = -1/3f(x) + 5, there is a vertical shift of 5 units. The "+ 5" term at the end of the function indicates that the function has been shifted up by 5 units.
Answer: (3) A. shifted up 5 units
To summarize the transformations:
(1) B. did not reflect over the x-axis
(2) B. less steep than the parent function
(3) A. shifted up 5 units
To compare the given linear function g(x) = -1/3f(x) + 5 to its parent function f(x) and determine the transformations, we need to understand the effect of each component of the new function.
1. To determine if the function has been reflected over the x-axis, we look at the coefficient in front of f(x). In this case, it is -1/3. Since the coefficient is negative, the function has been reflected over the x-axis. So the answer is (1) A. Reflected over the x-axis.
2. To determine if the function is steeper or less steep than the parent function, we look at the coefficient in front of f(x). In this case, it is -1/3. Compared to the parent function, the absolute value of -1/3 is smaller than 1. Hence, it is less steep than the parent function. So the answer is (2) B. less steep than the parent function.
3. To determine if the function has been shifted up or down, we look at the constant added at the end of the function, which is +5. Since the constant is positive, the function has been shifted up. So the answer is (3) A. shifted up 5 units.
In summary, the given linear function g(x) = -1/3f(x) + 5 has the following transformations:
(1) A. Reflected over the x-axis
(2) B. less steep than the parent function
(3) A. shifted up 5 units.