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HiSET Exponential Functions — practice questions

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

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Exponential Functions questions and exercises with answers

Showing questions 1–3 of 3.

In an exponential function, where does the variable sit?Read the answer and worked solution →Through which point does the graph of f(x) = a raised to the power x always pass?Read the answer and worked solution →Why is the base of an exponential function never allowed to be 1?Read the answer and worked solution →

Worked practice questions

In an exponential function, where does the variable sit?

  1. In the base part
  2. In the numerator
  3. In the coefficient
  4. In the exponent
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Correct answer: D. In the exponent

1. An exponential function is written as a fixed base raised to a variable power. 2. So the variable sits in the exponent rather than in the base. 3. That is the reverse of a power such as x squared, where the variable is the base. _Source: OpenStax Intermediate Algebra (CC BY 4.0), section 10.2 Evaluate and Graph Exponential Functions_

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Through which point does the graph of f(x) = a raised to the power x always pass?

  1. The point (1, 0)
  2. The point (0, 1)
  3. The point (0, 0)
  4. The point (1, 1)
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Correct answer: B. The point (0, 1)

1. Any allowed base raised to the power 0 gives 1. 2. So the output at an input of 0 is always 1, whatever the base. 3. That places the point (0, 1) on every such graph, which is the y-intercept. _Source: OpenStax Intermediate Algebra (CC BY 4.0), section 10.2 Evaluate and Graph Exponential Functions_

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Why is the base of an exponential function never allowed to be 1?

  1. It would give a negative rule
  2. It would give no y-intercept
  3. It would give a constant rule
  4. It would give a linear rule
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Correct answer: C. It would give a constant rule

1. An exponential function raises a fixed base to a variable power. 2. The number 1 raised to any power is still 1. 3. So a base of 1 would produce the same output for every input, which is a constant rule. 4. A constant rule has none of the growth or decay behaviour that exponential functions are used for. _Source: OpenStax Intermediate Algebra (CC BY 4.0), section 10.2 Evaluate and Graph Exponential Functions_

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More Mathematics topics

The Quadratic FormulaGraphing Quadratic FunctionsLogarithmic FunctionsApplications of Quadratic EquationsExponential and Logarithmic EquationsQuadratic InequalitiesSquare Root PropertyEquations in Quadratic Form