With these in mind, let's write the properties of the given graph.
We see that it
is an increasing function,
has an asymptote, x-axis, and
intercepts the y-axis at the point (0,5).
Additionally,
it seems that the point (- 1,2.5) lies on the curve and
the domain is all real numbers and the range is all positive real numbers.
We might assume that it is an exponential growth function. Then, since the y-intercept is the point (0,5), a is equal to 5.
y=a * b^x ⇔ y=5 * b^x
We know that the point ( - 1, 2.5) is on the curve. Let's substitute the point and find b.
Now we can write the function.
y=5 * b^x ⇔ y=5 * 2^x
Let's draw its graph using calculator.
we can enter it in the calculator by pushing Y= and writing the function.
Next, by pushing GRAPH, the calculator will draw the graph of the function.
We get the same graph. Therefore, the graph shows an exponential growth function.
