What is the range of the exponential function shown below? f(x)=11×(1/3)^x

The range of the given exponential function is (0,∞).

Step-by-step explanation:

The general form of an exponential function is

Where, a is initial value, b>1 is growth factor and 0<b<1 is decay factor.

The given function is

Here . It means the initial value of the function is 11 and the decay factor is . The value of is positive for all real values of x.

Multiply both sides by 11.

It means the value of F(x) is positive for all real values of x.

Range is the set of outputs. So, the range of the function all positive real number except 0.

Range = (0,∞)

Therefore the range of the given exponential function is (0,∞).

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).

the rocket cannot penetrate the ground, in a contextual sense, therefore the roots of this equation should be the domain of this function. i'll let you find the roots of this quadratic equation (hint: use the quadratic formula:  

1- c

2-a

step-by-step explanation:

mark brainliest!