Function Notation

Function notation is a way to represent a function using symbols. It typically uses the letter 'f' followed by parentheses containing the input variable, such as f(x).

To evaluate a function at a specific value, substitute the value into the function's equation in place of the variable. For example, to evaluate f(6) for f(x) = x + 5, replace x with 6: f(6) = 6 + 5 = 11.

This function represents the number of animal crackers left in a jar after x minutes if you eat 6 crackers per minute, starting with 200 crackers.

In the function h(t), k represents the initial height of the candle before it starts burning.

Substitute t = 3 into the function: 35 = -5(3) + k. Solve for k: k = 35 + 15 = 50.

To find h(-3), substitute -3 into the function: h(-3) = 3 - 2(-3)^2 = 3 - 18 = -15.

Substitute -2 into the function: f(-2) = (-2)^2 + 3 = 4 + 3 = 7.

The general form of a linear function is f(x) = mx + b, where m is the slope and b is the y-intercept.

The slope represents the rate of change of the function; it indicates how much the output value changes for a unit change in the input value.

The y-intercept is the value of the function when the input is zero (f(0)). It is the point where the graph of the function crosses the y-axis.