Question Which of the following exponential functions is increasing (from left to right)? Select all that apply. Select all that apply: $$ \square f(x)=\left(\frac{1}{8}\right)^{x} $$ $$ \square f(x)=(1.6)^{x} $$ $$ \square f(x)=(0.77)^{x} $$ $$ \square f(x)=(1.2)^{x} $$ $$ \square f(x) $$

Question

UpStudy AI · Accepted Answer

To determine which of the given exponential functions are increasing from left to right, we need to analyze the base of each function:

1. **Exponential functions of the form $$ f(x) = a^x $$**:
   - If $$ a > 1 $$, the function is increasing.
   - If $$ 0 < a < 1 $$, the function is decreasing.

Now, let's evaluate each function:

1. $$ f(x) = \left(\frac{1}{8}\right)^{x} $$
   - Base: $$ \frac{1}{8} $$ (which is less than 1)
   - This function is **decreasing**.

2. $$ f(x) = (1.6)^{x} $$
   - Base: $$ 1.6 $$ (which is greater than 1)
   - This function is **increasing**.

3. $$ f(x) = (0.77)^{x} $$
   - Base: $$ 0.77 $$ (which is less than 1)
   - This function is **decreasing**.

4. $$ f(x) = (1.2)^{x} $$
   - Base: $$ 1.2 $$ (which is greater than 1)
   - This function is **increasing**.

Based on this analysis, the increasing functions are:

- $$ \square f(x) = (1.6)^{x} $$
- $$ \square f(x) = (1.2)^{x} $$

So, the correct selections are:

- $$ \square f(x) = (1.6)^{x} $$
- $$ \square f(x) = (1.2)^{x} $$
The increasing functions are $$ f(x) = (1.6)^{x} $$ and $$ f(x) = (1.2)^{x} $$.

Question Which of the following exponential functions is increasing (from left to right)? Select all that apply. Select all that apply: \( \square f(x)=\left(\frac{1}{8}\right)^{x} \) \( \square f(x)=(1.6)^{x} \) \( \square f(x)=(0.77)^{x} \) \( \square f(x)=(1.2)^{x} \) \( \square f(x) \)

Real Tutor Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Pre Calculus Questions