Translations of Functions

Front

What is the effect of adding or subtracting a number on the INSIDE of a function's grouping symbols?

Back

It shifts the graph left or right, not up or down.

Front

What is the equation of a quadratic function translated left 4 units from the standard form y = x^2?

Back

y = (x + 4)^2

Front

If a function is translated right 1 unit and up 5 units, what is the general form of the translation?

Back

f(x) = f(x - 1) + 5

Front

What is the equation for the translation of f(x) = |x| that moves up 6 units?

Back

f(x) = |x| + 6

Front

What is the equation for the translation of f(x) = |x| that moves left 10 units and down 1 unit?

Back

f(x) = |x + 10| - 1

Front

What does the term 'translation' refer to in the context of functions?

Back

A translation refers to shifting the graph of a function horizontally and/or vertically without changing its shape.

Front

How does a vertical translation affect the graph of a function?

Back

It shifts the graph up or down depending on whether a positive or negative value is added.

Front

What is the effect of a horizontal translation on the graph of a function?

Back

It shifts the graph left or right depending on the sign of the value added or subtracted.

Front

What is the general form of a quadratic function?

Back

y = ax^2 + bx + c, where a, b, and c are constants.

Front

How do you determine the direction of a vertical shift in a function?

Back

If a positive number is added to the function, it shifts up; if a negative number is subtracted, it shifts down.