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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 $e$

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:36

Sketch the graph of the fu…

01:27

01:29

01:17

01:48

02:23

02:15

02:08

00:13

Sketch a graph of the give…

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00:14

03:00

01:55

02:51

The premise of this problem is understanding the parent function of the exponential function. Either The ex looks, you know, across the Y axis at 01 It doesn't cross the X axis. It's exponential growth and has a horizontal Aston Toda y equals zero. Um, and then when you know the transformations of why equals or f of X equals e to the X minus one minus three. And I like function notation, that's just my preference that we have two shifts going on. So we are shifting right? One that's from the exponents and then down. Three Most calculus students know these rules by now. Uh, so what that means is, instead of hitting the X Y axis at 01 we need to shift right one. So imagine counting to the right one and then down three, we'd be at the ordered pair. One negative tube. Um, and if we shift the horizontal, asked him to go down three 123 That's where your horizontal aspect to it would be at. Why equals negative three. And it's still a growth function, the basis still larger than one. Eso would be going up into the right just like this. I think that's all you need for this graph to get the right answer. It's

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