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22.06.2021 •
Mathematics
The black graph is the graph of y= f(x). Choose the equation for the red graph which one: a, b, c, d?
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Ответ:
Option C.
Step-by-step explanation:
First, let's define the transformations used here:
We can see that the red graph is shifted horizontally to the right, and that is reflected across the x-axis:
Horizontal shift:
For a general function f(x) an horizontal shift of N units is written as:
g(x) = f(x + N)
where:
If N > 0, the shift is to the left
if N < 0 , the shift is to the right.
Reflection across the x-axis.
For a function f(x), a reflection across the x-axis is just written as:
g(x) = -f(x)
So, if here we have a reflection across the x-axis and a horizontal shift of one unit to the right, we would write the equation for the red graph as:
g(x) = -f(x) (only for the reflection)
g(x) = -f(x - 1) (for the reflection and the shift)
Then the graph of the red function is:
y = -f(x - 1)
We can rewrite this as:
y = -1*f(x - 1)
dividing both sides by -1 we get:
y/-1 = f(x - 1)
This is what we can see in option C, so the correct option is C.
Ответ:
Step-by-step explanation:
the 2nd line can be rewritten as y < x-3
So, any value that is less than both 4x+4 and x-3 will work
Pick any value you want for x, and figure y possibilities
x=0; x-3=-3, 4x+4=4, so y<-3 ... (0,-5) will work
I'm sure you can now come up with other pairs.