MTH 111 Midterm

Tammy deposits the same amount of money into a bank account every month. The table below shows the amount of money in the account after different amounts of time.

1. How much money was already in the account when Tammy started depositing money? 197 2. As time increases, the amount of money in the account increases. At what rate is the amount of money in the account increasing? 17 dollars per month

Here is a graph of the function f. A. All values at which f has a local maximum B. All local maximum values of f

A. x-values where the maximums are B. y-values where the maximums are

The graph of a function is shown below. Find f(-2) and find one value of x for which f(x)=4.

x-values go inside the function and outpoint a y value. So the points would be (-2,2) and (0,4)

Look at the graphs and their equations below. Then fill in the information about the leading coefficient A, B, C, and D

Coefficient closest to 0 is widest graph Coefficient with greatest value is narrowest graph

A construction crew is lengthening a road. Let be the total length of the road (in miles). Let be the number of days the crew has worked. Suppose that gives as a function of . The crew can work for at most days. Identify the correct description of the values in both the domain and range of the function. Then, for each, choose the most appropriate set of values.

Domain is the x-values Range is the y-values

For each relation, decide whether or not it is a function.

Each input only has one output

For each graph below, state whether it represents a function.

Each x-value must have just one y-value

Suppose that the function f is defined, for all real numbers, as follows.

Find where each value lies, then input for that specific function

For each graph, choose the function that best describes it.

Honestly, just look in the notebook

The functions f, g, and h are defined as follows.

Just input the values into the function

What are the leading coefficient and degree of the polynomial?

Leading Term: the term with the largest exponent Leading Coefficient: the coefficient of the leading term (just the number) Degree: The largest exponent

Rewrite each equation as requested.

Logx(a)=b is rewritten as x^b=a x^b=a is rewritten as logx(a)=b

The graphs of the functions g and h are shown below. For each graph, find the absolute maximum and absolute minimum. If no such value exists, click on "None"

Look at the y-values, list those

Write the domain and range of F as intervals or unions of intervals.

Open circle is ( ), closed circle is [ ] Domain is x-values, look left to right Range is y-values, look bottom to top, write down the largest range

The function is defined as follows.

Simply into the value into the function

The number of bacteria in a culture increases rapidly. The table below gives the number N(t) of bacteria at a few times t (in hours) after the moment when N=1000

Use the average rate of change formula. (y2-y1)/(x2-x1)

For each function, determine whether it is a polynomial function.

What aren't functions: -There can't be negative exponents -No exponentials ex. 3^x -No square roots on the x cause the equals (x)^1/2, a fraction -Can't have fractioned exponents on x

Determine the interval(s) on which the function is (strictly) decreasing.

Write the x-values for when the graph is decreasing

Transform it to make the graph of

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The graph of a rational function f is shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "holes".

x and y intercepts: look at where the line crosses both axis. Asymptotes: Vertical is where the x-value approaches, horizontal is where the y-value approaches Domain is the x-values Range is the y-values

Translate each graph as specified below

f(x)=(x-6): Shift right by 6, add 6 to x-values f(x)=(x+6): Shift left by 6, subtract 6 from x-values f(x)=x-6: Lower by 6, subtract 6 from y-values f(x)=x+6: Raise by 6, add 6 to y-values