Write the equation for the absolute value parent function that has these transformation:
shift left 4
shift down 3
vertical compression by 2
1/2 (|x+4| - 3)
or
1/2 |x+4| - 3
depending on the order in which the transformations are applied
Alright, let me get my clown glasses on to solve this one!
Starting with the general equation for the absolute value parent function, which is y = |x|, let's apply the given transformations:
1. Shift left 4: This means we need to replace x with (x + 4) to shift the graph 4 units to the left.
2. Shift down 3: To shift the graph 3 units down, we subtract 3 from the expression. So far, our equation becomes y = |x + 4| - 3.
3. Vertical compression by 2: To compress the graph vertically, we multiply the entire expression by 1/2. Now the equation is y = (1/2)|x + 4| - 3.
Voilà! The equation for the absolute value parent function with the given transformations is y = (1/2)|x + 4| - 3.
The equation for the absolute value parent function is y = |x|.
To apply the given transformations, we will start with the parent function and perform the transformations step by step.
1. Shift left 4 units:
To shift the function left 4 units, we replace x with (x + 4):
y = |x + 4|
2. Shift down 3 units:
To shift the function down 3 units, we subtract 3 from the function:
y = |x + 4| - 3
3. Vertical compression by 2:
To vertically compress the function by a factor of 2, we divide the entire function by 2:
y = (1/2)(|x + 4| - 3)
Therefore, the equation for the transformed absolute value function with a left shift of 4, a downward shift of 3, and a vertical compression by 2 is y = (1/2)(|x + 4| - 3).
To write the equation for the absolute value parent function with the given transformations, let's start with the equation for the absolute value parent function, which is:
f(x) = |x|
Now, let's apply the given transformations step by step:
1. Shift left 4: To shift the function left by 4 units, we need to replace "x" with "(x + 4)".
f(x) = |x + 4|
2. Shift down 3: To shift the function down by 3 units, we need to subtract 3 from the entire equation.
f(x) = |x + 4| - 3
3. Vertical compression by 2: To vertically compress the function by 2, we need to divide the entire equation by 2.
f(x) = (|x + 4| - 3)/2
Therefore, the equation for the absolute value parent function with the given transformations is f(x) = (|x + 4| - 3)/2.