Question
Which function is increasing?
f(x) = (1/15)^x
f(x) = (0.5)^x
f(x) = 5x
f(x) = (1/5)^x
f(x) = (1/15)^x
f(x) = (0.5)^x
f(x) = 5x
f(x) = (1/5)^x
Answers
Answered by
GPT-4o mini
To determine which function is increasing, let's examine each of the given functions individually:
1. **\( f(x) = (1/15)^x \)**: This function is of the form \( a^x \) where \( 0 < a < 1 \). Functions where the base is a fraction between 0 and 1 decrease as \( x \) increases. Therefore, this function is **decreasing**.
2. **\( f(x) = (0.5)^x \)**: Similar to the previous function, this is also of the form \( a^x \) where \( 0 < a < 1 \). This function also decreases for increasing \( x \), so it is **decreasing**.
3. **\( f(x) = 5^x \)**: This function is of the form \( a^x \) where \( a > 1 \). Such functions increase as \( x \) increases. Therefore, this function is **increasing**.
4. **\( f(x) = (1/5)^x \)**: Again, this is of the form \( a^x \) where \( 0 < a < 1 \). Therefore, this function is **decreasing**.
In conclusion, the **increasing function** among the given options is **\( f(x) = 5^x \)**.
1. **\( f(x) = (1/15)^x \)**: This function is of the form \( a^x \) where \( 0 < a < 1 \). Functions where the base is a fraction between 0 and 1 decrease as \( x \) increases. Therefore, this function is **decreasing**.
2. **\( f(x) = (0.5)^x \)**: Similar to the previous function, this is also of the form \( a^x \) where \( 0 < a < 1 \). This function also decreases for increasing \( x \), so it is **decreasing**.
3. **\( f(x) = 5^x \)**: This function is of the form \( a^x \) where \( a > 1 \). Such functions increase as \( x \) increases. Therefore, this function is **increasing**.
4. **\( f(x) = (1/5)^x \)**: Again, this is of the form \( a^x \) where \( 0 < a < 1 \). Therefore, this function is **decreasing**.
In conclusion, the **increasing function** among the given options is **\( f(x) = 5^x \)**.