Question

Help with finding these equation of a graph?

Answer 1

Well the original one looks like this

Answer 2

the one they show is merely a reflection over the x-axis of the original meaning all the y values are negative

Answer 3

Here is a plot of the original and the new equation

Answer 4

If you plot the original 2^x it looks like the red curve. to make it look like your version, you have to multiply by a negative number. If you look at a few points on the original and where they end up on the new curve, it looks like multiplying by -2 does the trick notice that -2*2^x can be written a different way: -1* 2^1 * 2^x you can "add exponents" if you have the same base (of 2) -1 * 2^(x+1) or
\[ −2^{x+1}\]

Answer 5

so I should choose all negative numbers for x?

Answer 6

Can you ask your question a different way?

Answer 7

I don't really understand what to do yet. Do I need to plug in negative numbers for x?

Answer 8

The question asks for the equation of the graph plotted. They tell you the "parent function" is y= 2^x

I would first (roughly) plot the parent function:
at x= -1 y = 2^(-1) = 1/2 (-1, 0.5)
x=0, y=2^0 = 1 (0,1)
x=1, y=2^1 = 2 (1,2)

when x gets (say 10) y= 2^10 = 1024 y gets big very fast
when x gets small say -10, y= 2^(-10)= 1/1024 or about 0.001
I would sketch this curve (close to zero when x is negative, and zooming up when x gets big)

next I look at the graph they showed. it is close to zero when x is minus, but it is below the x-axis.... it zooms, but it zooms down. y gets very negative.
to get the original graph to do that, we can multiply by -1.

Answer 9

if we multiply the parent function by -1 we would get
y = -1* x^2
at x= -1 y = -1*2^(-1) = -1/2 (-1, -0.5)
x=0, y=-2^0 = 1 (0,-1)
x=1, y=-2^1 = 2 (1,-2)

I see that this graph goes through (0,-1) and (-1,-0.5)
but the graph we wants goes through (0,-2) and (-1, -1)
How do I get 0,-1 to turn into 0,-2 we could add -1 to it. but if we add -1 to that point we have to add -1 to all the points, and (-1,-0.5) turns into (-1,-1.5) which does not match (-1,-1)

another way to get 0,-1 to turn into 0,-2 is multiply by 2)
that works. so a good guess is the equation we want is -2 * parent function

y = -2 * 2^x

Answer 10

I'm sorry I still don't understand this :/