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NSC / Matric Functions — practice questions

Explore 3 free Functions questions in NSC / Matric Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Functions questions and exercises with answers

Showing questions 1–3 of 3.

A vertical line drawn across the graph of a relation cuts it twice. What does that show?Read the answer and worked solution →What must be true of a function before its inverse is also a function?Read the answer and worked solution →How can the logarithm of a number raised to a power be rewritten?Read the answer and worked solution →

Worked practice questions

A vertical line drawn across the graph of a relation cuts it twice. What does that show?

  1. The relation is a function
  2. The relation is not a function
  3. The relation has no inverse
  4. The relation is a straight line
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Correct answer: B. The relation is not a function

1. A function gives exactly one output value for each input value. 2. A vertical line collects every point of the graph that shares one input value. 3. Two crossings therefore mean that one input value has two different outputs. 4. That breaks the definition, so the relation is not a function. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 2: Functions_

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What must be true of a function before its inverse is also a function?

  1. It must be a many to one relation
  2. It must pass through the origin
  3. It must be a one to one relation
  4. It must be a straight line graph
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Correct answer: C. It must be a one to one relation

1. Finding an inverse means swapping the input and output values around. 2. If two different inputs shared one output, the swap would give one input with two outputs. 3. That result would fail the definition of a function. 4. So the original function has to pair each output with exactly one input, which is a one to one relation. 5. A many to one relation is exactly the case that fails, so that option is wrong. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 2: Functions_

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How can the logarithm of a number raised to a power be rewritten?

  1. The power plus the logarithm
  2. The logarithm of the power
  3. The power over the logarithm
  4. The power times the logarithm
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Correct answer: D. The power times the logarithm

1. The logarithmic laws are built directly on the exponential laws. 2. Raising a number to a power repeats a multiplication, and logarithms turn multiplication into addition. 3. Repeated addition of the same logarithm is the same as multiplying that logarithm by the power. 4. So the logarithm of a number raised to a power is the power multiplied by the logarithm of the number. 5. Adding the power instead would mix a plain number in with a logarithm, which is not a valid step. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 2: Functions_

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