Graph and Properties of the Exponential Function
Which formula matches the graph in the picture?
Correct answers
To bronze: 0 of 5
Daily streak
To Busy Bee: 0 of 3 days
Today: 0 of 5 exercises
An exponential function has the variable x in the exponent: y = 2ˣ. For x = 1, 2, 3, 4 it gives 2, 4, 8, 16 — every step to the right doubles the value. With base ½ it is the other way round: every step halves the value. The graph always passes through the point (0, 1), because a⁰ = 1.
What does this generator do?
On the easy level you get the formula y = aˣ and decide whether the function is increasing or decreasing, what its range is, which point lies on the graph and which line is the asymptote. On the medium level you match the formula y = aˣ + n to a graph. On the hard level the graph is also shifted left or right: y = a^(x − m) + n.
How to use it
1) Look at the base: if it is greater than 1, the function increases; if it is between 0 and 1, it decreases. 2) The horizontal asymptote is y = n — that is how far the graph is shifted up or down. 3) The point where the exponent is zero is (m, 1 + n). 4) Move 1 to the right from it: the value becomes a + n, which tells you the base.