2. The graph of an exponential function f(x) with base a is...

2. The graph of an exponential function f(x) with base a is shown below: f(x) = a^x (0,1) (-1, a^-1) a. Is a>1 or is 0<a<1? b. Give the domain and range of f. c. Sketch the graph of g(x) = a^x + 3. d. Give the domain and range of g. e. Sketch the graph of h(x) = a^(x+4) f. Give the domain and range of h.

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00:01 Okay, couple questions about this graph.

00:03 So let's see.

00:05 First question is a, is my base greater than one or between zero and one? this base has to be between zero and one because this graph is what we call strictly decreasing.

00:21 As we read it from left to right, it's doing nothing but getting smaller.

00:25 So that means my base has to be a value between zero and one.

00:30 Want.

00:32 Domain and range.

00:33 Well, for this function, the domain is all real numbers.

00:40 So negative infinity to positive infinity.

00:43 You can plug in whatever you want for that x variable.

00:48 But no matter what you plug in, you're never going to get anything below the x -axis.

00:54 You're never going to touch the x -axis.

00:56 So your range is zero to infinity, entirely above the x -axis.

01:01 Axis sketch the graph of a of act a to the x rather plus three so i'm just going to do it right on top of this grid so this graph is at zero one this point so if i want to go up three i'm going to just go three units up the x axis and i'm going to this so this is a to the x x so this is a to the x plus three.

01:35 You just take that graph and shift it three units up.

01:40 So now what does that mean for the domain and the range? okay, well, your domain is going to remain all real numbers...

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