Change in Linear and Exponential Functions - AP Precalculus

0.5. The number being raised to the power.

1.1. The base represents growth when greater than 1.

0.8. The base represents decay when between 0 and 1.

1. Substitute $x = 2$: $f(2) = 6(2) - 9 = 3$.

$f(x) = 2x - 5$. Form $mx + b$ indicates linear function.

1. The coefficient of $x$ is the rate of change.

Linear function. Linear functions have constant slope.

$f(x) = 2 \times 3^x$. Form $a \times b^x$ indicates exponential function.

1. Substitute $x = 2$: $f(2) = 2 \times 3^2 = 18$.

Decreasing function. Negative slope means function decreases as $x$ increases.

Function decreases. Negative exponent creates reciprocal, decreasing function.

$12$. Y-intercept occurs when $x = 0$.

1. Substitute $x = 2$: $f(2) = 6(2) - 9 = 3$.

$f(x) = mx + b$. Standard form with slope $m$ and y-intercept $b$.

Initial value. Y-intercept is the starting value when $x = 0$.

Exponential function. Exponential functions have constant multiplicative rate.

1. The constant term is the y-intercept.

1. The coefficient multiplying the exponential term.

Linear function. Linear functions have constant slope.

1. The slope is the coefficient of $x$.

1. The base of the exponential term.

1. Substitute $x = 3$: $f(3) = 4 \times 2^3 = 32$.

Increases the growth rate. Larger base means faster exponential growth.

Rate of change. Slope shows how much $y$ changes per unit of $x$.

Initial value. Y-intercept is the starting value when $x = 0$.

Exponential function. Exponential functions have constant multiplicative rate.

$f(x) = 2x - 5$. Form $mx + b$ indicates linear function.

$f(x) = 2 \times 3^x$. Form $a \times b^x$ indicates exponential function.

1. Slope = $\frac{6-2}{3-1} = \frac{4}{2} = 2$.