Solving exponential function

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An exponential function has the form of f(x) = a^x, where x is a variable and a is a constant which is called the base of the function. A should be greater than 0.

  • Properties of the exponential function depend on the value of a.
  • A never crosses the x-axis.
  • When a = 1, the graph is presented by a horizontal line at y = 1.
  • When a is between 0 and 1, we graph it this way:

    Graph step 1
  • When a is above 1, here’s the graph we have:

    Graph step 2


Sketch the graph of f(x) = 2^x and g(x) = $\(frac{1}{2})^x$ on the same axis system.


First, we have to pick some values of x and do some function evaluations.

Therefore, here is the sketch of the two graphs:

Two graphs


Sketch the graph of h(t) = $1 - 5e^{1 - \frac{t}{2}}$



Make a table of values for this function.



Plot the graph.

Graph solution