Here are four graphs. Graph A Graph B Graph C Graph D The graphs represent four different types of function $f(t)$. Match each description of the function in the table to the letter of its graph. Description of function Graph $f(t)$ is inversely proportional to $x$ $f(t)$ is a trigonometrical function $f(t)$ is an exponential function $f(t)$ is directly proportional to $ oot{2} x$

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Here are four graphs - Edexcel - GCSE Maths - Question 18 - 2019 - Paper 3

Question 18

Here are four graphs. Graph A Graph B Graph C Graph D The graphs represent four different types of function $f(t)$. Match each description of the function in th... show full transcript

Worked Solution & Example Answer:Here are four graphs - Edexcel - GCSE Maths - Question 18 - 2019 - Paper 3

Step 1

Match $f(t)$ is inversely proportional to $x$

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Answer

Graph D is a hyperbola, which indicates an inverse relationship. Therefore, $f(t)$ is inversely proportional to $x$ .

Step 2

Match $f(t)$ is a trigonometrical function

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Answer

Graph B exhibits oscillatory behavior typical of trigonometric functions, such as sine and cosine. Hence, $f(t)$ is a trigonometrical function.

Step 3

Match $f(t)$ is an exponential function

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Answer

Graph A shows a rapid increase which is characteristic of exponential functions. Therefore, $f(t)$ is an exponential function.

Step 4

Match $f(t)$ is directly proportional to $ oot{2} x$

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Answer

Graph C appears linear and shows a positive increase, consistent with directly proportional functions. Thus, $f(t)$ is directly proportional to $oot{2} x$ .

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