Question

the function f(x)=a^x+4 will never cross the x-axis

Answer 1

True

Explanation:

This is true!

The following function:

$f(x)=a^x+4$

is an exponential function that will never cross the x-axis. So let's test some characteristic values in order to understand this.

• When x approaches zero:

In this case, we will have the y-intercept, so:

$f(0)=a^0+4 \\ \\ f(0)=1+4 \\ \\ f(0)=5$

• When x approaches ∞:

In this case, the function grows without bound, so:

$f(x)=a^{\infty}+4 \\ \\ f(x)=\infty$

• When x approaches -∞:

In this case, the function tends to 4:

$f(x)=a^{-\infty}+4 \\ \\ f(x)=0+4 \\ \\ f(x)=4$

In conclusion, the range is $(4, \infty)$ so the graph never touches the x-axis.

Learn more:

y-intercept: https://brainly.com/question/13889768#

#LearnWithBrainly

Answer 2

Answer:

True

Step-by-step explanation:

Since it is a positive 4 the x-axis will never be cross, if the 4 was a negative the a-axis would be crossed.

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