IB Mathematics Applications & Interpretation Topic SL 2.3—graph of a Function Questionbank (SL/HL)

Question 1

SLPaper 1

Consider the function $y = ln (x^{2} - 2 x - 3)$ .

1.

Draw a sketch, clearly indicating its domain, the equations of any asymptotes and any points where the graph intersects the coordinate axes.

[4]

2.

Utilizing your graph or an analytical method, find the solution to the inequality $∣ y ∣ \leq ln 3$ .

[5]

Question 2

SLPaper 1

A quadratic function has $y$ -intercept 1, an $x$ -intercept at $x = 1$ , and the $x$ -coordinate of its vertex is 3. The equation of the quadratic function is in the form $y = a x^{2} + b x + c$ .

1.

Write down the value of $c$ .

[1]

2.

Write down the second $x$ -intercept of the function.

[2]

3.

Find the values of $a$ and $b$ .

[4]

Question 3

HLPaper 1

The function $f$ is defined by $f (x) = 2 x^{3} + 5$ , $- 2 \leq x \leq 2$ .

1.

Write down the range of $f$ .

[2]

2.

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

[2]

3.

Write down the domain and range of $f^{- 1}$ .

[2]

Question 4

HLPaper 1

Let $f (x) = x^{2} + 2 x + 1$ and $g (x) = x - 5$ , for $x \in R$ .

1.

Expand and simplify $f (x) - 5$ .

[2]

2.

Find $f (8)$ .

[2]

3.

Solve $x^{2} + 2 x - 4 = 0$ .

[3]

Question 5

SLPaper 1

Consider the curve $y = - x^{3} - 6 x^{2} + 15 x + 4$ .

1.

Find $\frac{d y}{d x}$ .

[2]

2.

Determine the $x$ -coordinates of the stationary points.

[3]

3.

Classify each stationary point as a local maximum or local minimum.

[3]

4.

Sketch the graph for $- 7 \leq x \leq 3$ , indicating the stationary points and the $y$ -intercept.

[2]

IB Mathematics Applications & Interpretation SL 2.3—graph of a Function Questionbank

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IB Mathematics Applications & Interpretation SL 2.3—graph of a Function Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 2.3—graph of a Function Questionbank

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