If the point (4,-1) is a point on the graph of f then f

Mathematics

2 answers:

Ostrovityanka [42]2 years ago

8 0

B. thats all i know seems how you only gave so little info

AlekseyPX2 years ago

3 0

If the point (4,-1) is a point on the graph of y = f(x). The corresponding point on the graph of y = g(x) is: (4,-1/2), (2,-1), (-1,-1), (1,4), (4,-4), (-12,1)

$g(x) = \frac{1}{2} f(x)$ => (4,-1/2)
$g(x) = f(x-2)$ => (2,-1)
$g(x) = f(-x)$ => (-1,-1)
$g(x) = f(4x)$ => (1,4)
$g(x) = 4f(x)$ => (4,-4)
$g(x) = -f(x)$ => (-12,1)

<h3>Further explanation </h3>

Dividing the function by 2 divides all the y-values by 2 as well. So to get the new point, we will take the y-value (-1) and divide it by 2 to get 2. Therefore, the new point is (4,-1/2)
Subtracting 2 from the input of the function makes all of the x-values increase by 2 (in order to compensate for the subtraction). We will need to add 2 to the x-value (4) to get 2. Therefore, the new point is (2,-1)
Making the input of the function negative will multiply every x-value by 1. To get the new point, we will take the x-value (4) and multiply it by -1 to get. Therefore, the new point is (-1,-1)
Multiplying the input of the function by 4 makes all of the x-values be divided by 4 (in order to compensate for the multiplication). We will need to divide the x-value (4) by 4 to get 1. Therefore, the new point is (1,4)
Multiplying the whole function by 4 increases all y-values by a factor of 4 , so the new y-value will be 4 times the original value (4) or -4. Therefore, the new point is (4,-4)
Multiplying the whole function by -1 also multiplies every y-value by -1, so the new y-value will be -1 times the original value (-1). or 1. Therefore, the new point is (-12,1)

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