It moves the graph down by 1/4
I used demos and the graph had a change making it lower coordinates by a fourth.
-14x cause you are flipping it over to the y_axis
We have been given the equation of the linear parent function as: .
We are asked to write an equation of the new function that is vertically stretched by a factor of 4 and flips over the x-axis.
Rule for vertical stretching of a function is:
, where a is the factor of stretching.
After stretching our parent function by a factor of 4 our new function will be:
Now we will flip or reflect our function over x-axis by the rule: as reflecting a function over x-axis, its x-coordinate remains same but y-coordinates become negative.
After flipping our function over x-axis our new function will be:
Therefore, after a vertical stretching by a Factor of 4 and flipping over the x-axis, our new function will be .
The given function is
The translation is defined as
Where, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
It is given that f(x) shifts 4 units left and 2 units up. So,
Substitute a=4 and b=2 in equation (1).
Therefore, the new function is .
For a function in the form f(x) = x, we can say:the function f(x) = ax is a vertical stretch if a>1 and compress if 0<a<1the function -f(x) is the original, flipped over x-axis
keeping the 2 rules in mind, we can say that
vertical stretch by a factor of 3 would make it f(x) = 3x
flip over x-axis would make it f(x) = -3x
answer choice D is right
Equation of the new function becomes f(x) =
We are given the function f(x) = x.
The first transformation applied on this f(x) is 'vertical compression by 1/4' i.e. f(x) becomes .
This transformation shrinks the graph of f(x) towards x-axis.
Now, the next transformation applied to is 'a flip over the y-axis' i.e. 'reflection over y-axis'
This transformation takes the mirror image of the function over y-axis.
Hence, the equation of the new function becomes f(x) = and the final graph is shown below.
f(x) = |x + 4| + 2.
When you shift the function to the left, the x-value changes, so you put the change within the absolute value. Also, within the absolute value, when you shift things to the right, you minus, and when you shift to the left, you add.
When you shift the function up, the y-value changes, so you put the changes outside of the absolute value. Shifting up means adding and shifting down means subtracting.
Hope this helps!
f(x)= -14x is the right answer.had the same question tkl