11th Grade Q1

To determine the $y$-intercept of an exponential function, you find the point where the graph crosses the $y$-axis. This happens when the input value $x=0$.

An exponential function typically has the form:

where:

• $a$ is a constant multiplier,
• $b$ is the base of the exponential,
• $x$ is the variable (exponent),
• $c$ is a constant shift.

The $y$-intercept is the value of $f(x)$ when $x=0$.

Method

1. Substitute $x=0$

To find the $y$-intercept, substitute $x=0$ into the function:

Since $b^0=1$, this simplifies to:

2. Write the intercept as a point

The $y$-intercept is the point where the graph crosses the $y$-axis. It is written as:

Example

Let’s find the $y$-intercept of $f(x)=4\cdot 3^x-5$.

1. Substitute $x=0$:
   

1. The $y$-intercept is:
   

Key Points to Remember

• The $y$-intercept is found by substituting $x=0$ into the function.
• The $y$-intercept is always written as a point $(0,f(0))$.
• For exponential functions, the $y$-intercept is influenced by both the constant $a$ (multiplier) and the shift $c$.