Question

given the parent function f(x)=ab^x how could changing from a 2 to -2 cause f(x) to change? use words like "increasing" "decreasing" "positive" "negative" "domain" and "range" to describe the similarities and differences in the graph

Answer 1

Here, we want to get the response of the given function with respect to the change in the value of the leading coefficient

As we can see from the question, what we have is an example of an exponential function

Generally, with exponential function with a positive value for a, as the value of x moves closer to negative infinity, we have that the value of f(x) moves closer to 0. What this mean is that with a decrease in the value of x, the value of f(x) moves closer to 0

Hence, as the domain value moves closer to negative infinity, the value of the range moves closer to 0. Furthermore, as the value of the domain moves closer to positive infinity, the value of the range also close in on positive infinity

The above situation is for a being positive (given as 2)

Now, when a becomes negative, we have an opposite direction for the plot

Although, as the domain value moves closer to negative infinity, we have the value of f(x) being closer to zero. This is directly as above

However, as the domain moves towards positive infinity, the value of the range moves closer to negative infinity

In summary;

`\begin{gathered} \text{for a = 2} \\ x\Rightarrow\text{ +}\infty\text{ , f(x)}\Rightarrow+\infty \\ x\Rightarrow-\infty,\text{ f(x) }\Rightarrow0 \\ \text{for a = -2} \\ x\Rightarrow+\infty,\text{ f(x)}\Rightarrow-\infty \\ x\Rightarrow-\infty,\text{ f(x)}\Rightarrow0 \end{gathered}`