Transformations can make it tricky to understand the intercepts of a function. Let’s break down how different transformations affect these intercepts:
Vertical Shifts: When we move a function up or down by a number ( k ), we create a new function called ( f(x) + k ). This change alters the ( y )-intercept. So, it might be hard to find out where it crosses the ( y )-axis without doing some calculations.
Horizontal Shifts: If we move a function left or right by a number ( h ), we write it as ( f(x - h) ). This shift changes the ( x )-intercept. To find the new intercept, we have to work out new ( x ) values, which can be confusing.
Stretches and Compressions: When we stretch or compress the function up and down, we write it as ( af(x) ). This transformation affects the ( y )-intercept too. If the value of ( a ) is 1, the ( y )-intercept may stay at the same ( y )-value.
To make things easier, it's helpful to recalculate the intercepts after making these transformations. This way, we can clearly see how the function changes!
Transformations can make it tricky to understand the intercepts of a function. Let’s break down how different transformations affect these intercepts:
Vertical Shifts: When we move a function up or down by a number ( k ), we create a new function called ( f(x) + k ). This change alters the ( y )-intercept. So, it might be hard to find out where it crosses the ( y )-axis without doing some calculations.
Horizontal Shifts: If we move a function left or right by a number ( h ), we write it as ( f(x - h) ). This shift changes the ( x )-intercept. To find the new intercept, we have to work out new ( x ) values, which can be confusing.
Stretches and Compressions: When we stretch or compress the function up and down, we write it as ( af(x) ). This transformation affects the ( y )-intercept too. If the value of ( a ) is 1, the ( y )-intercept may stay at the same ( y )-value.
To make things easier, it's helpful to recalculate the intercepts after making these transformations. This way, we can clearly see how the function changes!