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what are the domain and range of the function?

f(x)=12x+5√

domain: [−5, ∞)

range: (−∞, ∞)

domain: [0, ∞)

range: (−5, ∞)

domain: (−5, ∞)

range: (0, ∞)

domain: [−5, ∞)

range: [0, ∞)

Domain [-5,∞)

Range [0,∞)

Step-by-step explanation:

Part 1) Find the domain

we have

we know that

The radicand must be greater than or equal to zero

so

solve for x

subtract 5 both sides

The solution for x is the interval [-5,∞)

All real numbers greater than or equal to -5

Remember that

The domain of a function is the set of all possible values of x

therefore

The domain of the function f(x) is the interval  [-5,∞)

Part 2) Find the range

we have

Find the value of f(x) for the minimum value of x

For x=-5

The minimum value of f(x) is equal to zero

so

The solution for f(x) is the interval [0,∞)

All real numbers greater than or equal to 0

Remember that

The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.

therefore

The range of the function is the interval [0,∞)

slope is 35 and 20 miles is the y-intercept.

step-by-step explanation:

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).