# Exam-Style Questions on Graphing Functions

## Problems on Graphing Functions adapted from questions set in previous exams.

### 1.

IGCSE Extended

The table shows some values (rounded to one decimal place) for the function $$y=\frac{2}{x^2}-x, x\neq 0$$.

 $$x$$ $$y$$ -3 -2 -1 -0.5 0.5 1 2 3 4 3.2 2.5 8.5 7.5 1 -2.8

(a) Complete the table of values.

(b) Draw the graph of $$y=\frac{2}{x^2}-x$$ for $$-3\le x \le -0.5$$ and $$0.5\le x\le 4$$.

(c) Use your graph to solve the equation $$\frac{2}{x^2}-x-3=0$$

(d) Use your graph to solve the equation $$\frac{2}{x^2}-x=1-2x$$

(e) By drawing a suitable tangent, find an estimate of the gradient of the curve at the point where x = 1.

(f) Using algebra, show that you can use the graph at $$y=0$$ to find $$\sqrt[3]2$$

### 2.

IB Standard

Let $$f (x)=a(x-b)^2+c$$. The vertex of the graph of $$f$$ is at (4, -3) and the graph passes through (3, 2).

(a) Find the value of $$c$$.

(b) Find the value of $$b$$.

(c) Find the value of $$a$$.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

The solutions to the questions on this website are only available to those who have a Transum Subscription.

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Friday, January 26, 2018

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The text passage contains exam-style questions on graphing functions, including tasks to complete a table of values, draw a graph, solve equations using the graph, estimate the gradient, and show algebraic relationships.
multiple_questions
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
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- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Exam-Style Questions on Graphing Functions

## Problems on Graphing Functions adapted from questions set in previous exams.

### 1.

IGCSE Extended

The table shows some values (rounded to one decimal place) for the function $$y=\frac{2}{x^2}-x, x\neq 0$$.

 $$x$$ $$y$$ -3 -2 -1 -0.5 0.5 1 2 3 4 3.2 2.5 8.5 7.5 1 -2.8

(a) Complete the table of values.

(b) Draw the graph of $$y=\frac{2}{x^2}-x$$ for $$-3\le x \le -0.5$$ and $$0.5\le x\le 4$$.

(c) Use your graph to solve the equation $$\frac{2}{x^2}-x-3=0$$

(d) Use your graph to solve the equation $$\frac{2}{x^2}-x=1-2x$$

(e) By drawing a suitable tangent, find an estimate of the gradient of the curve at the point where x = 1.

(f) Using algebra, show that you can use the graph at $$y=0$$ to find $$\sqrt[3]2$$

### 2.

IB Standard

Let $$f (x)=a(x-b)^2+c$$. The vertex of the graph of $$f$$ is at (4, -3) and the graph passes through (3, 2).

(a) Find the value of $$c$$.

(b) Find the value of $$b$$.

(c) Find the value of $$a$$.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

The solutions to the questions on this website are only available to those who have a Transum Subscription.

Exam-Style Questions Main Page

Search for exam-style questions containing a particular word or phrase:

To search the entire Transum website use the search box in the grey area below.

Kausar Begum Khan, Kenya

Friday, January 26, 2018

"This is a fabulous website! I cannot thank you enough."

Tuesday, November 6, 2018

"Transum is so resourceful. The resources are so child-friendly that my students love its usage.It has a wide range of topics and caters to most of my needs. 'Thankyou" will be too small a word to express my gratitude to the content developers of this site."

Ahmed Jaja, Ghana

Thursday, November 22, 2018

"It was very useful for me.I recommend it to every math student.Thank you."

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

For Students:

For All:
user
The text passage contains exam-style questions on graphing functions, including tasks to complete a table of values, draw a graph, solve equations using the graph, estimate the gradient, and show algebraic relationships.

TYPE: MULTIPLE_QUESTIONS