Transformation of curves - Higher - OCR test questions - OCR

1

How is the graph of y = x² + a obtained from the graph of y = x²?

Translation parallel to the x-axis

Translation parallel to the y-axis

Reflection in the y-axis

2

The diagram shows the graph of y = √x in green. What is the equation of the red graph?

A graph showing -1 to 5 on the y axis and -1 to 9 on the x axis. y = √x is plotted as 0, 3 with a green curve and y = √x + 2 plotted with a pink curve from 2, 5.

y = √x + 2

y = \(\sqrt{x + 2}\)

y = 2√x

3

How is the graph of y = (x + a)² obtained from the graph of y = x²?

Translation parallel to the x-axis

Translation parallel to the y-axis

Reflection in the y-axis

4

The diagram shows the graph of y = √x in green. What is the equation of the red graph?

A graph showing -1 to 3 on the y axis and -2 to 9 on the x axis. y = is represented in green from 0, 3 and is then shown two units to the left, parallel to the x axis in pink from -2, 3.

y = √x – 2

y = 2

y = \(\sqrt{x + 2}\)

5

Describe the transformation that -f(x) represents on the graph of f(x)?

Translation in the x-direction

Reflection in the x-axis

Reflection in the y-axis

6

The diagram shows the graph of y = √x in red. What is the equation of the green graph?

A graph showing -3 to 3 on the y axis and -1 to 9 on the x axis. y = is represented in pink from 0, 3 and is then shown reflected in the x axis in green from 0, -3.

y = √(-x)

y = -√x

y = √x

7

How is the graph of y = (-x)² obtained from the graph of y = x²?

Translation parallel to the y-axis

Reflection in the x-axis

Reflection in the y-axis

8

The diagram shows the graph of y = √x in red. What is the equation of the green graph?

A graph showing -4 to 4 on the y axis and -8 to 8 on the x axis. y = √x is represented in pink on the right of the graph and is then shown reflected in the y axis on the left in green.

y = √(-x)

y = -√x

y = √x

9

How is the graph of y = (x + 2)² + 3 obtained from the graph of y = x²?

a translation of \(\begin{pmatrix} 2 \\ -3 \end{pmatrix}\)

a translation of \(\begin{pmatrix} -2 \\ -3 \end{pmatrix}\)

a translation of \(\begin{pmatrix} -2 \\ 3 \end{pmatrix}\)

10

The diagram shows the graph of y = √x in red. What is the equation of the green graph?

A graph showing -2 to 4 on the y axis and -1 to 9 on the x axis.

y = \(\sqrt{x - 1} - 1\)

y = \(\sqrt{x + 1} + 1\)

y = \(\sqrt{x - 1} + 1\)