SEKOLAH BUKIT SION AY 2021-2022

CHAPTER 2 TEST: GRAPHS OF FUNCTIONS

Name: ________________________ Class: __________ Date: _______________ Problem 1 Match the graph with its type by writing the CAPITAL letter on the space provided. [5]

______ Cubic Function ______ Reciprocal Function

______ Quadratic Function ______ Exponential Function

______ Linear Function

A B C

D E

Problem 2 A sum of $5000 is invested in an account that pays 4% annually. How much is in the account after 6 years if the money is a) compounded monthly?

Answer: _______________________ [3] b) compounded annually?

Answer: _______________________ [3] Problem 3 An SUV that is originally worth $50,000 depreciates at a rate of 29.5% every year. Find a function for the depreciation of the SUV, and how much will it be worth after 3 years?

Answer: _______________________ [3] Problem 4 Give a formula for the exponential function f(x) has the values in the next table.

x 0 1 2 3 4 f(x) 5 15 45 135 405

Answer: _______________________ [2]

Problem 5 The graph of 𝑦 = 100 ∙ 3! is shown below.

(a) Find the value of x if y = 600.

Answer: _______________________ [1]

(b) This graph can be used to illustrate the growth of a certain bacteria which increases by a multiplier of 3, daily. If the initial population is 100, estimate after how many days will the bacteria’s population reaches 500000. Write your answer correct to 2 decimal places.

Answer: _______________________ [2]

Problem 6 Shown below is the graph of the function 𝑦 = 2"! + 𝑥.

(a) By drawing a tangent and showing your complete working, find the gradient of the curve at x = –3.

Answer: _______________________ [3]

(b) By drawing a suitable straight line, solve the equation 2"! + #$𝑥 − 2 = 0.

Answer: _______________________ [3]

Problem 7 The diagram below shows the graph of y = f(x) = 𝑥$ − $

!− 2.

(a) Write down an equation of the asymptote of f(x) = 𝑥$ − $!− 2.

Answer: _______________________ [1]

(b) Use the graph provided to find

(i) the value of y if x = –2

Answer: _______________________ [1]

(ii) the values of x of y = 5

Answer: _______________________ [2]

(c) For each equation to be solved below, write down the equation of the line that must be used and must be drawn to find the values of x graphically.

On the grid, draw a suitable line to solve the equation.

(i) 𝑥$ − $

!− 2 = 0

Equation of straight line: _______________________ [1]

x = _________ or x = __________ [2]

(ii) 𝑥$ − $!− 2 = 1

Equation of straight line: _______________________ [1]

x = _________ or x = __________ [2]

(iii) 𝑥$ − $!− 7 = −3𝑥

Equation of straight line: _______________________ [1]

x = _________ or x = __________ [2]

Problem 8

(a) Complete the table of values for 𝑦 = %!− 1. [3]

x –5 –4 –3 –2 –1 0 1 2 3 4 5

y –3 –3.7 –5 7

(b) On the grid, draw the graph of 𝑦 = %!− 1f for −5 ≤ 𝑥 ≤ 5. [4]

(c) By drawing a suitable straight line, use the graph in part (b) to solve the equation 𝒙𝟐 = 𝟒 + 𝒙.

Equation of straight line: ____________________ [3]

Answers: x = ___________ or x = ___________ [2]