Start with the graph of the appropriate basic exponential...

Start with the graph of the appropriate basic exponential function f and use transformations to sketch the graph of the function g. State the domain and range of g and the horizontal asymptote of its graph. g(x) = 2^x + 5 Use the graphing tool to graph the function. What is the domain of g(x)? (Type your answer in interval notation.) What is the range of g(x)? (Type your answer in interval notation.) What is the equation for the horizontal asymptote? (Type an equation.)

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00:01 So the first thing they want us to do is they want us to start with the graph of the appropriate basic function to help us graph g of x equals 2 raised to the x.

00:09 Well, the basic graph would just be our base 2 raised to the x.

00:12 So i'll call that f of x.

00:14 So f of x would equal 2 to the x.

00:16 Well, define values for y, you can substitute in values for x and evaluate them.

00:22 Well, when x is equal to 0, anything to the 0 is 1.

00:25 So that would be our y intercept.

00:27 If i substituted 1 for x, 2 to the 1 1 is 2.

00:31 If i substitute in 2 for x, 2 squared would equal to 4, so 2 .4 would be a point.

00:37 If we substitute in 3, 2 to the 3rd is 8, so 3 .8 would be a point.

00:42 And if i plugged in negative 1, that would be 2 to the negative 1, which is 1 1⁄2.

00:46 So notice that this graph is going to decrease as we go to the left.

00:51 So now we have our basic f -of -x function.

00:54 So now let's use this to graph g of x.

00:57 We'll notice in our exponent we're adding 5.

00:59 Well, in this case, what that's going to do is going to shift our graph to the left five units.

01:05 So that means what typically our order, our y intercept was at 01, that point will shift over five units to the left...

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