Graph transformations

Describe the single transformation which maps the curve with the equation

y = ln x

onto the curve with the equation

y = 2 ln x

Tick () one box.

Stretch, scale factor 2, parallel to the y-axis

Stretch, scale factor , parallel to the x-axis

Describe a sequence of two transformations which maps the graph with equation

onto the graph with equation

State the equation of the vertical asymptote of the graph with equation

It is given that

f (x) = x (x – a)(x – 6)

where 0 < a < 6

Sketch the graph of y = f(x) on the axes below.

Sketch the graph of y = f(–2x) on the axes below.

The curve with equation y ln x is transformed by a stretch parallel to the x-axis with scale factor 2

Find the equation of the transformed curve.

Circle your answer.

The graph of y f (x) is shown below.

One of the four equations listed below is the equation of the graph y f (x)

Identify which one is the correct equation of the graph.

Tick () one box.

Sketch the curve with equation

The polynomial p (x) is given by

It is given that x 3 is a factor of p(x)

Use the factor theorem to show a 2

State the transformation which maps the curve with equation

onto the curve with equation

The polynomial x²(2x 2) 36 can be written as (x 3)(2x² bx c)

Without finding the values of b and c, use your answers to parts (a) and (b)(ii) to explain why

The curve

is transformed by a stretch, scale factor 2, parallel to the y-axis.

State the equation of the curve after it has been transformed.

Circle your answer.

one direction.

Beth thinks the stretch should be in the y-direction.

Paul thinks the stretch should be in the x-direction.

State, giving reasons for your answer, whether Beth is correct, Paul is correct, both are correct or neither is correct.

A function f is defined for all real values of x as

The function has exactly two stationary points when x 0 and x

f x 9 (a) (i) Find ()

Determine the nature of the stationary points.

Fully justify your answer.

State the range of values of x for which

is an increasing function.

A second function g is defined for all real values of x as

State the single transformation which maps f onto g.

The graph of y f (x) is shown below.

Sketch the graph of y f (x)

Sketch the graph of y 2f (x) 4

Identify the graph of y 1 x 2 from the options below.

Tick () one box.

The graph of y 5^x is transformed by a stretch in the y-direction, scale factor 5

State the equation of the transformed graph.

Circle your answer.