# What is the range of the function y=4e^x?

## Answers

The range of the exponential function y=4e^x is all real numbers greater than 0 (first option)

Solution: The range of a function is the values of the dependent variable "y". In the case of a exponential function of the form y=a^x, you will get for "y" numbers greater than 0:

y=e^x → Range is all real numbers greater than 0

and if you multiply by 4:

y=4e^x, you will obtain numbers greater than 0, then:

Range of the function y=4e^x is all the real numbers greater than 0.

(0, ∞)

Step-by-step explanation:

As x becomes increasingly negative, e^x decreases towards zero (but never touches zero). As x grows without bound, e^x increases without bound.

Thus, the range is (0, ∞).

All real numbers greater than 0

Step-by-step explanation:

All real numbers greater than 0

Step-by-step explanation:

We have been given the function [tex]y=4e^x[/tex]

Range is the set of y values for which the function is defined.

Now, solve the equation for x and then see which real values of y we can take.

[tex]y=4e^x[/tex]

Divide both sides by 4

[tex]e^x=\frac{y}{4}[/tex]

Take natural log both sides

[tex]\ln(e^x)=\ln(\frac{y}{4})\\\\x=\ln(\frac{y}{4})[/tex]

logarithmic function is defined for positive values only.

Thus, we have

[tex]\frac{y}{4}0\\\\y0[/tex]

Hence, range is all real numbers greater than 0

the answer (B) thank me later ;)

the range of function [tex]4e^{x}[/tex] is (0, ∞)

Step-by-step explanation:

Function range definition:-

The set of values of the dependent variable for which a function is defined

we need to find the range of function [tex]4e^{x}[/tex]

The range of an exponential function of the form [tex]n^{ax+b}+k[/tex] is [tex]f(x)k[/tex]

[tex]k=0[/tex]

As x grows without bound, [tex]e^{x}[/tex] increases without bound.

Thus, the range is (0, ∞).

{ y | y > 0 }

Range ⇒ Values that can 'come out' of the function.

As x → -∞, y → 0

As x → +∞, y → ∞

This means that the smallest value that can come out of the function is a value which is tiny but greater than 0 and the largest is ∞ so the range is option 1, all real numbers greater than 0.

(When I get these questions it always helps me to think of the graph to work out what y approaches as x approaches -∞ and +∞)

Try going to this symbolab.com/solver/algebra-calculator

Your answer is f(y) > 0

A is your answer