Questions and Answers on Functions Paper Example

Q1: Rewrite the following relationships using function notation.

An airplane needs to travel 400 km. Determine a function for the speed of the airplane, with respect to time.

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S = where S=speed, d=distance and t=time

An ice cream cone is left sitting in the hot sun. Sarah notices that the ice cream melts and loses half of its volume every 5 minutes. If the starting volume was 125 mL, determine a function for the volume, with respect to the amount of time left out in the sun.

Taking the reduction to follow a linear model, the y intercept will be the volume at the starts; which is 125ml. the slope for reduction in volume will be the difference in volume against the difference in time giving the slope as. But linear models are defined as y=mx+c, where m is gradient and c is the start volume. Therefore the function will be

Scott wants to calculate the distance from his house to each of his friends' houses. If he drives at 50 km/h, find a function for the distance, with respect to the number of hours it takes to travel.

d= s*t where s=speed (in km/h), d=distance (in km) and t=time (in h)

Q2: Find the inverses of each of the functions below algebraically

p(r)= ; say p(r) is q then

Replacing q and r and equating to zero gives which can be equated to

Using quadratic formula where now, and. Therefore, which comes to but q and r were interchanged so that

Therefore,

3y + 5x = 18 implies that y =

Replacing x and y implies x=; solve for y such that: x-6=

Therefore, . Implying that:

Therefore, the inverse of 3y + 5x = 18 is:

h(t) =

Say h(t) = s such that s=. Implies that replacing s with t and equating to zero gives

Using quadratic formula where now, and. Therefore, which comes to but q and r were interchanged so that

Therefore,

Q3: With the aid of graphs, explain whether or not the inverses in question 2 are functions.

The inverse is not a function since the x coordinates of the inverse have more than one y coordinate related to it, using the vertical line test

The inverse is a function since the x coordinates have only one y coordinate related to it using the vertical line test

The inverse is not a function since the x coordinates have more than one y coordinate related to it using the vertical line test

Q4: For each of the functions below, state the domain and range, the restrictions, the intervals of increasing and decreasing, the roots, y-intercepts, and vertices.

Range =, Domain =, y- intercept = (0,-8), increasing intervals =, decreasing interval = roots = (1,-6) vertex is given by (2,0) and (-2,0).

Range =, Domain =, y-intercept =, increasing interval =, decreasing interval =, roots = (2, 0)

Range =, Domain =, y-intercept = , increasing interval =, decreasing interval =, roots = (0,-1) and (2, 3)

Q5: The point (1,-2) is on the graph of f(x). Describe the following transformations on f(x), and determine the resulting point.

By multiplying the function by a constant the transformation that occurs compresses or expands the curvature of the function. This would result into an expansion of the curve

By adding a value to the x variable, the transformation that occurs is a transposition of the curve function. The curve would be transposed to the right of the x axis.

By negating the whole function, the transformation that occurs reflects the curve along the x axis.

By multiplying the x value by a negative value, the transformation that occurs flips the curve along the y axis.