F(x)=3x+1 (preimage)
g(x)=x+1 (image)
it is undergoing a reduction/compression with translation.
In general, a linear transformation is
g(x) = a*f(bx-h)+k
h=horizontal translation (right if h>0, left if h<0, note formula has minus sign)
k=vertical translation (up if k>0, down if k<0)
a=vertical stretching, (stretching if |a|>1, compression if |a|<1, also, if a<0, a reflection across the x-axis is performed)
b=horizontal stretching (|b|>0 compression, |b|<0 stretching, also, if b<0, a reflection across the y-axis is performed)
In this case,
g(x)=f(x/3), so it is a horizontal stretching.
Note that the y-intercept remains unchanged.
Answer:
9.8 ( to the nearest tenth )
Step-by-step explanation:
calculate the distance using the distance formula
d = √( x₂ - x₁ )² + ( y₂ - y₁ )²
with (x₁, y₁ ) = (- 7, - 5) and (x₂, y₂ ) = (- 3, 4)
d =
=
=
= 9.8
Answer:
B.
Step-by-step explanation:
First, let's start from the parent function. The parent function is:

The possible transformations are so:
,
where a is the vertical stretch, b is the horizontal stretch, c is the horizontal shift and d is the vertical shift.
From the given equation, we can see that a=1 (so no change), b=3, c=-3 (<em>negative </em>3), and d=3.
Thus, this is a horizontal stretch by a factor of 3, a shift of 3 to the <em>left </em>(because it's negative), and a vertical shift of 3 upwards (because it's positive).
Answer:
Step-by-step explanation: