f(2) = 5 f(3) = 2(3) + 1 f(3) = 7 Linear, Quadratic, and Exponential Function Graphs Linear Quadratic Exponential Description: Straight line U Shape (parabola) that Grows/Shrinks fast and opens up or down levels off on 1 side Graph looks like: Equation y = 2x y = 3x2 - 8 y = 2x How to tell from The x term is to the The x term is to the second The x term is the exponent the equation (x) power (x2) (2x) what the graph looks like: Graph specific In the equation y = mx + b, If the number with the x2 is In the equation y = ax , if a is information: if m is negative, the line negative, the U shape bigger than 1 the curve will decreases (goes down) as opens down. If the number grow fast. If a is between 0 we look from left to with the x2 is positive, the U and 1, the curve will shrink y = - x + 5 shape opens up: fast. If m is positive, the line increases (goes up) as we look from left to right: y = .5x + 2 Finding the x and y Intercepts in a Linear Function To find the x intercepts in a linear function like y = 2x + 6, we are going to set y = 0 and solve for x. To find the y intercept, we’ll set x = 0 and solve for y: x Intercept Set y = 0 and solve for x: y = 2x + 6 0 = 2x + 6 - 6 = 2x -3 = x
f(2) = 5 f(3) = 2(3) + 1 f(3) = 7 Linear, Quadratic, and Exponential Function Graphs Linear Quadratic Exponential Description: Straight line U Shape (parabola) that opens up or down Grows/Shrinks fast and levels off on 1 side Graph looks like: Equation y = 2x y = 3x2 - 8 y = 2x How to tell from the equation what the graph looks like: The x term is to the (x) The x term is to the second power (x2) The x term is the exponent (2x) Graph specific information: In the equation y = mx + b, if m is negative, the line decreases (goes down) as we look from left to y = - x + 5 If m is positive, the line increases (goes up) as we look from left to right: y = .5x + 2 If the number with the x2 is negative, the U shape opens down. If the number with the x2 is positive, the U shape opens up: In the equation y = ax , if a is bigger than 1 the curve will grow fast. If a is between 0 and 1, the curve will shrink fast. Finding the x and y Intercepts in a Linear Function To find the x intercepts in a linear function like y = 2x + 6, we are going to set y = 0 and solve for x. To find the y intercept, we’ll set x = 0 and solve for y: x Intercept Set y = 0 and solve for x: y = 2x + 6 0 = 2x + 6 - 6 = 2x -3 = x