Assume a car uses gas at a constant rate. After driving 25 miles since a full tank of gas was purchased, there was 9 gallons of gas left; after driving 70 miles since a full tank of gas was purchased, there was 7.2 gallons of gas left. Use a function to model the amount of gas in the tank (in gallons). Let the independent variable be the number of miles driven since a full tank of gas was purchased. Find this function’s domain and range in this context.

Q: Express the function graphed on the axes below as a piecewise function.

A: The graph is,

Q: Is the function even, odd, or neither?

A: From the graph of the given function, it is observed that the graph is symmetric about origin. Or it…

Q: If 150 bags are demanded per month when the price is $75 per bag and the amount demanded fell to 100…

A: Equation of a line passing through the point (a,b) and (c,d) is given by: y-d=m(x-c)    OR…

Q: Explain why every nonconstant linear function has an inverse.

A: Given: A linear function has an inverse.

Q: Differentiate the function: f(x) = x44x

A: We assume u and v, then find u' and v'

Q: Determine all the 1-linear functions δ: M1×1(F)→F.

A: Given mapping is,

Q: Evaluate the function at each specified value of the independent variable and simplify

A:

Q: Write the height h of the rectangle as a function of x.

A: In two-dimension cartesian-coordinate system, the value of a function at a point represented by the…

Q: is the function even, odd, or neither?

A:

Q: Differentiate the function.  f(x) = 240

A: Given function is

Q: Find the domain of the function : 1/√(x+2)

A:

Q: Describe what is meant by a piecewise linear function.

A: A piecewise linear function is a function composed of straight-line sections. It is a…

Q: Let f(x)=2x²-3x+1, find the valu

A:

Q: Find the Domain and Range of functions:

A:

Q: Write the linear function f for which f(1) = 3 and f(4) = 0.

A: Write the linear function f for which f(1) = 3 and f(4) = 0.

Q: for each dollar a driver spends on gas she can drive 15 miles assume she bought her car with 20000…

A: Given: for each dollar a driver spends on gas, she can drive 15 miles. Assume she bought her car…

Q: Which table does not represent a function of x?

A:

Q: Give the domain of the function:

A:

Q: a rectangular plot requires 2000 feet ( in feet ) of fencing to enclose it. if one of its dimensions…

A:

Q: The sum of two positive numbers is 210, then the function that models the product of the numbers is…

A: Let x be a positive number Given that: Sum of two positive numbers = 210

Q: Is the function odd, even, or neither

A:

Q: Find the function F

A:

Q: Differentiate the function with respect to the independent variable. f(x)=-7x+5x³-6 f(x) =

A: Given, f(x)=-7x4+5x3-6

Q: Determine whether the function (shown in the table below) could be linear or cannot be linear. A -…

A: The coordinates of points of the function are shown in the table given in the problem. For 1st and…

Q: Plot the fallawinet function:-

A:

Q: Find the linear function with the following properties.

A: A linear function is in the form of y = f(x) = mx+c where m is slope and c is y-intercept.

Q: Suppose f is a linear function such that f(3) = 5 and f(9) = -4. Find the equation for f. (Use x as…

A:

Q: Determine if the function h(x)=11x* – 2x² is even, odd or neither

A: We can check the function even or odd or neither as below.

Q: 2 2 V 4 +x-

A:

Q: Evaluate the function f(x)=2x+4 When x={2,3,7}

A:

Q: Find the domain of the function and express as an interval

A: In the question it is asked to calculate the domain of the function f(x)=x+6-2.

Q: Differentiate the function with respect to the independent variable. f(x) = (x° - 7x) 5 f'(x) = D

A: Given:

Q: is the function odd, even, or neither?

A:

Q: Classify the functions as even, odd, or neither. ƒ(x) = 3x

A:

Q: Draw the function!- メ+ー

A: Graph the function y=x+1

Q: h (x) = x" – xV2

A: We have to differentiate the function: hx=xπ-x2 We know the formula of differentiation,…

Q: Indicate whether the two functions are equal. If the two functions are not equal, then give an…

A: The given 2 functions are as follows. f:Z×Z→Z where fx,y=x+y g:Z×Z→Z where gx,y=x+y Both the…

Q: Differentiate the function. f(x) = 240 f'(x) =

A:

Q: A function wherein all terms are of the same degree in terms of x and y is known as ________

A:

Q: Differentiate the given function fcx) = (1-3ex)²

A:

Q: Apply the definition to differentiate the following functions: 1- y = ₁ 2- y = √√x 3-y=4-x²

A:

Q: Is the function one-to-one?

A:

Q: Describe an example of a real-live application of functions of two or more variables.

A:

Q: Determine whether the equation x2 + y2 = 25 defines y as a function of x.

A: Given equation x2+y2=25 Solve the above equation, we get x2+y2=25y2=25-x2y=±25-x2 In the above…

Q: Differentiate the function.   f(x)  =240

A: We have to differentiate the function: fx=240 We know that differentiation of any constant is zero.…

Q: Evaluate the function f(x)=x+4 when x=3

A: To evaluate the function f(x)=x+4 when x=3

Q: Differentiate the function. h(x) 4 xS - 4x3 + 1)8 5, x5 – 4x³ + h'(x) = %3!

A: We will use chain rule to solve this problem;

Q: Differentiate the function with respect to the independent variable. f(x) = 6 – 5x - 8x? f'(x) =O

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.