What does the equation $$y = \frac{1}{2}f(x)$$ represent?

This represents a vertical compression of the function $$f(x)$$ by a factor of 1/2.

What does the equation $$y = -f(x)$$ represent?

This represents a reflection of the function $$f(x)$$ across the x-axis.

How do you translate a function to the right?

To translate a function to the right, you subtract a constant from the input. For example, $$f(x - c)$$ shifts the graph right by c units.

How do you translate a function to the left?

To translate a function to the left, you add a constant to the input. For example, $$f(x + c)$$ shifts the graph left by c units.

What is the general form of a quadratic function?

The general form of a quadratic function is $$y = ax^2 + bx + c$$ , where a, b, and c are constants.

What does the equation $$y = \frac{1}{2}(x - 3)^2 + 4$$ represent?

This represents a quadratic function translated right 3 units and up 4 units, with a vertical compression by a factor of 1/2.

What is the effect of a negative coefficient in front of a function?

A negative coefficient reflects the graph of the function across the x-axis.

What does the equation $$y = \frac{1}{3}\text{sqrt}(x)$$ represent?

This represents a vertical compression of the square root function by a factor of 1/3.

What is the transformation of the function $$f(x) = x^2$$ to $$g(x) = (x + 2)^2 - 5$$ ?

The transformation shifts the graph of $$f(x)$$ left 2 units and down 5 units.

What is the significance of the vertex in a quadratic function?

The vertex is the highest or lowest point of the parabola, depending on the direction it opens.

Parent Function Transformations Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is a parent function?

Back

A parent function is the simplest form of a function in a family of functions, which can be transformed to create other functions in that family.

2.

FLASHCARD QUESTION

Front

How does a horizontal transformation affect a function?

Back

A horizontal transformation moves the graph of the function left or right.

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