# Natural Exponential Graphs

$$\large y=e^x$$

Natural Exponential Graphs also follow the rule of translations and transformations.

### Example 1

Sketch the graphs of $y=e^x$ and $y=-e^x$.
Reflected the $x$-axis.

### Example 2

Sketch the graphs of $y=e^x$ and $y=-e^{-x}$.

### Example 3

Sketch the graphs of $y=e^x$ and $y=e^{-x}$.

### Example 4

Sketch the graphs of $y=e^x$ and $y=e^{x+1}$.
Translated to left.

### Example 5

Sketch the graphs of $y=e^x$ and $y=3 \times e^{x}$.
Multiplied 3 times to the $y$ values.

### Example 6

Sketch the graphs of $y=e^x$ and $y=e^x+1$.
Translated to up.

### Example 7

Sketch the graphs of $y=e^x$ and $y=e^{x-1}$.
Translated to right.

### Example 8

Sketch the graphs of $y=e^x$ and $y=e^{x+1}-1$.
Translated to left and down.

### Example 9

Sketch the graphs of $y=e^x$ and $y=e^x-1$.
Translated to down.

### Example 10

Sketch the graphs of $y=e^x$ and $y=e^{x-1}+1$.
Translated to right and up. ## Exponential Graphs

Functions of the form exponential, where the base is a positive real number other than 1 are called exponential graphs or exponential functions.

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