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Sketch the graph of the function defined by the given equation.$$y=f(x)=e^{x+1}-3.$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 3

The Number $e$

Campbell University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

01:48

Sketch the graph of the fu…

01:37

01:17

01:29

01:27

02:23

02:15

02:08

00:13

Sketch a graph of the give…

00:35

00:14

02:58

02:51

02:00

02:25

01:55

right. So as we're tasked with finding the either the X plus one, uh, minus three graph is what we're supposed to graph. The whole premise of this problem is understanding, uh, the parent function of E to the X. Because either the X is an exponential growth function, though if you plug in zero for X, it makes perfect sense the Y intercept to be one. Either the zero power was one. The base of E is larger than to, uh well, we only care that's larger than one. So it's exponential growth. Uh uh, and it has a horizontal asking toda y equals zero. So when I look at this graph and I see plus three to the X, I know that we're going to take that graph. We're going to shift left one unit and the minus on the outside here means we're going to shift down three units. So my graph, instead of hitting at 01 01 I need to go left one and then down 12 three because remember, I'm going down three from y equals one andan. Also, I need to move my horizontal ass from tow down three 123 And so as you look at that, uh, it's still exponential growth. So it goes up into the right. I don't know exactly where it crosses the Y axis. Something like that. Um, this is all you really need. Thio have the correct craft.

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