91Ó°ÊÓ

The y-intercept of a function is the point where the graph of the equation crosses the y-axis. This happens when the value of the input variable (x) is zero. To find the y-intercept for the function given in the exercise, we substitute x = 0 into the function formula. The function provided is a constant function, written as \( f(x) = 5 \).

Substitute x = 0 into the function:
\( f(0) = 5 \)

This shows that when x is zero, the output value (y) is 5. So, the y-intercept of the function \( f(x) = 5 \) is the point (0, 5).

To summarize:

• The y-intercept occurs where x=0.
• In the function \( f(x) = 5 \), the y-intercept is located at (0, 5).

The x-intercept is the point where the graph crosses the x-axis. This occurs when the output of the function (f(x) or y) is zero. To find the x-intercept, set the function equal to zero and solve for x.

In the given exercise, the function is a constant function, which is expressed as \( f(x) = 5 \). This means the function's value does not change; it is always 5 no matter what value x takes.

To find the x-intercept, set the function equal to zero:
\( 5 = 0 \)

This equation is not possible since 5 never equals 0. Therefore, the function \( f(x) = 5 \) does not intersect the x-axis.

To summarize:

• The x-intercept occurs where the function's output \( f(x) = 0 \).
• For \( f(x) = 5 \), there are no x-intercepts since 5 does not equal 0.

A constant function is a type of function where the output value is the same for all input values. It is usually written in the form \( f(x) = c \), where c is a constant number. This means that no matter what x-value you substitute into the function, the result will always be c.

In the given exercise, the function is \( f(x) = 5 \). This indicates that for every input value of x, the function will output a value of 5.

Characteristics of a constant function include:

• Its graph is a horizontal line.
• There is no variation in the output value.
• The slope of the graph is zero.

Because it is a horizontal line, it doesn't matter what x-value you choose, the y-value will always be the constant c.

Understanding constant functions helps in recognizing that they have a simple, unchanging output, which makes finding intercepts straightforward.