IB Maths AA SL/Question Bank/2.1 Functions - SL content

IB Maths AA SL 2.1 Functions - SL content Question Bank

SL245 questions10 previewsSyllabus linked

[Maximum number: 6]

Let f(x)=p(x-q)(x-r). Part of the graph of f is shown below.

The graph passes through the points (-2,0),(0,-4) and (4,0).

(a)

Write down the value of q and of r.

[ 2 ]

(b)

Write down the equation of the axis of symmetry.

[ 1 ]

(c)

Find the value of p.

[ 3 ]

[Maximum number: 10]

Let $f(x)=8 x-2 x^{2}$ . Part of the graph of f is shown below.

(a)

Find the x-intercepts of the graph.

[ 4 ]

(b)

(i)

Write down the equation of the axis of symmetry.

[ 3 ]

(ii)

Find the y-coordinate of the vertex.

[ 3 ]

[Maximum number: 4]

Let f(x)=2 x+4 and $g(x)=7 x^{2}$ .

(a)

Find $(f \circ g)(x)$ .

[ 2 ]

(b)

Find $(f \circ g)(3.5)$ .

[ 2 ]

[Maximum number: 6]

Let f be a quadratic function. Part of the graph of f is shown below.

The vertex is at P(4,2) and the y-intercept is at Q(0,6).

(a)

Write down the equation of the axis of symmetry.

The function f can be written in the form $f(x)=a(x-h)^{2}+k$ .

[ 1 ]

(b)

Write down the value of h and of k.

[ 2 ]

(c)

Find a.

[ 3 ]

[Maximum number: 5]

Let f(x)=3 x, g(x)=2 x-5 and $h(x)=(f \circ g)(x)$ .

(a)

Find h(x).

[ 2 ]

(b)

Find $h^{-1}(x)$ .

[ 3 ]

[Maximum number: 5]

Let f(x)=7-2 x and g(x)=x+3.

(a)

Find $(g \circ f)(x)$ .

[ 2 ]

(b)

Write down $g^{-1}(x)$ .

[ 1 ]

(c)

Find $\left(f \circ g^{-1}\right)(5)$ .

[ 2 ]

[Maximum number: 6]

Let f(x)=4 x-2 and $g(x)=-2 x^{2}+8$ .

(a)

Find $f^{-1}(x)$ .

[ 3 ]

(b)

Find $(f \circ g)(1)$ .

[ 3 ]

[Maximum number: 5]

Let f(x)=2 x+3 and $g(x)=x^{3}$ .

(a)

Find $(f \circ g)(x)$ .

[ 2 ]

(b)

Solve the equation $(f \circ g)(x)=0$ .

[ 3 ]

[Maximum number: 7]

Let $f(x)=x^{2}+x-6$ .

(a)

Write down the y-intercept of the graph of f.

[ 1 ]

(b)

Solve f(x)=0.

[ 3 ]

(c)

On the following grid, sketch the graph of f, for $-4 \leq x \leq 3$ .

[ 3 ]

[Maximum number: 5]

Let $f(x)=a(x-h)^{2}+k$ . The vertex of the graph of f is at (2,3) and the graph passes through (1,7).

(a)

Write down the value of h and of k.

[ 2 ]

(b)

Find the value of a.

[ 3 ]