Transforming functions is like giving them a fresh new look! When we change a function, we are really changing how it looks both on a graph and in its formula. Let’s break it down:
Moving Up and Down: You can shift a function up or down by adding or subtracting a number. For example, if you have ( f(x) = x^2 ), then changing it to ( f(x) + 3 = x^2 + 3 ) moves the graph up by 3 units.
Moving Left and Right: To move a function left or right, you need to change the input value. For instance, with ( f(x - 2) = (x - 2)^2 ), the graph shifts to the right by 2 units.
Stretching and Squeezing: To stretch or squeeze a function up and down, you multiply by a number. So if you take ( f(x) = x^2 ) and change it to ( 2f(x) = 2x^2 ), the graph stretches up by a factor of 2.
Flipping: To flip a function, you make its output negative. For example, if you have ( f(x) = -x^2 ), this flips it across the x-axis.
By learning about these transformations, you can see how changes in the formula will change the graph!
Transforming functions is like giving them a fresh new look! When we change a function, we are really changing how it looks both on a graph and in its formula. Let’s break it down:
Moving Up and Down: You can shift a function up or down by adding or subtracting a number. For example, if you have ( f(x) = x^2 ), then changing it to ( f(x) + 3 = x^2 + 3 ) moves the graph up by 3 units.
Moving Left and Right: To move a function left or right, you need to change the input value. For instance, with ( f(x - 2) = (x - 2)^2 ), the graph shifts to the right by 2 units.
Stretching and Squeezing: To stretch or squeeze a function up and down, you multiply by a number. So if you take ( f(x) = x^2 ) and change it to ( 2f(x) = 2x^2 ), the graph stretches up by a factor of 2.
Flipping: To flip a function, you make its output negative. For example, if you have ( f(x) = -x^2 ), this flips it across the x-axis.
By learning about these transformations, you can see how changes in the formula will change the graph!