# How do you find the vertical intercept

## Calculate the y-intercept

### y-axis intercept for any functions

If you cannot read the y-axis intercept from the function equation, you can use the following property to calculate the y-axis intercept:

The **y-intercept** corresponds to the \ (y \) value at the position \ (x = 0 \).

Let's look at some examples.

### Fractional rational function

The function is given

\ [f (x) = \ frac {x ^ 2 + 4} {x + 1} \]

If we insert \ (x = 0 \) into the function

\ [f ({\ color {red} 0}) = \ frac {{\ color {red} 0} ^ 2 + 4} {{\ color {red} 0} +1} = \ frac {4} {1 } = 4 \]

we get the y-intercept

\ (y = 4 \)

### Natural exponential function (exponential function)

The function is given

\ (f (x) = e ^ x \)

If we insert \ (x = 0 \) into the function

\ (f ({\ color {red} 0}) = e ^ {{\ color {red} 0}} = 1 \)

we get the y-intercept

\ (y = 1 \)

*Note:* According to the power laws, \ (x ^ 0 = 1 \) applies.

### Natural logarithm (ln function)

**example 1**

The function is given

\ (f (x) = \ ln (x) \)

If we insert \ (x = 0 \) into the function, we find:

\ (f ({\ color {red} 0}) = \ ln ({\ color {red} 0}) \)

**Attention!** The definition set of the natural logarithm is \ (D =] 0; \ infty [\).

The function is therefore not defined at the point \ (x = 0 \).

**Example 2**

\ (f (x) = \ ln (x + 5) \)

If we insert \ (x = 0 \) into the function

\ (f ({\ color {red} 0}) = \ ln ({\ color {red} 0} + 5) = \ ln (5) = 1.61 \)

we get the y-intercept

\ (y = 1.61 \)

In summary, it can be said that the y-axis intercept is the y-coordinate of the point of intersection of a function graph with the y-axis. The y-axis intercept is calculated by inserting \ (x = 0 \) into the function. With some functions you can read the y-axis intercept directly from the function equation.

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