1. graphing exponential functions

I don't know how to graph this. The x as an exponent is throwing me off. How do you solve this?

Sketch the graphs of y= -5'x (negative 5 to the power x) and y=-5'x+2_-1(negative 5 to the power x+2, minus one) on the same set of axes and identify the domains, ranges, any asympototes, and y-ints.

2. Originally Posted by dcfi6052
I don't know how to graph this. The x as an exponent is throwing me off. How do you solve this?

Sketch the graphs of y= -5'x (negative 5 to the power x) and y=-5'x+2_-1(negative 5 to the power x+2, minus one) on the same set of axes and identify the domains, ranges, any asympototes, and y-ints.
Just to be clear, the first one is $y = (-5)^x$ or $y = -5^x$? (Same question about the second one.)

I'm going to assume it's the second option because the first can get us into some technical difficulties.

When in doubt, plot a series of points.
(x, -5^x)
(-3, -1/125)
(-2, -1/25)
(-1, -1/5)
(0,-1)
(1, -5)
(2, -25)
(3, -125)
.
.
.

As far as domains are concerned, find any x values that the function cannot take. (Typically when using a simple exponential function like the one you are using there are no problems, so the domain is all real numbers.)

For ranges, exponential functions usually trail off to an asymptote either at positive or negative infinity, so look for this.

I have attached the graph for both functions. Note that the blue function is simply the red one shifted two units to the left (from the (x+2)) and down one unit (from the -1).

-Dan