For a question like this, treat it just like you would the use of a numeric value for evaluating your function. All you do is “plug in” . Thus, for this function, you get:

From here, you merely need to distribute correctly!

“The square of the sum” means that the summation of the terms is done first, and that summation is squared, which corresponds to the term .

In order to find , work from the inside out. In other words, begin by finding , or  since 

Now, seeing as . Substitute  for  in  in order to find the answer. 

Start on the inside by finding  when . 

Now that we know , we can substitute  for  in . 

Find .

Substitute -1 for  in the given function.

If you didn’t remember the negative sign, you will have calculated 36. If you remembered the negative sign at the very last step, you will have calculated -36; however, if you did not remember that  is 1, then you will have calculated 18.

The company's binding process incorporates a fixed fee; therefore, we must use the formula for a linear equation:

The fixed fee means that the consumer pays a single fee of $2.25 to bind the book regardless of how many pages that book has; thus, the fixed fee is represented by the y-intercept, or b, of the equation. The problem states that each page will cost an additional $0.15 per page, which varies with depending on the number of pages in the book. The page cost is represented by the slope, m, of the equation. In order to calculate the total cost, , you must multiply the number of pages, p, by $0.15 and add the fixed cost of $2.25; therefore, the following equation accurately models the cost of binding a book:

We can take each of the listed transformations of  one at a time. If  is to be shifted up by four units, increase every value of  by 4. 

Next, take this equation and reflect it across the x-axis. If we reflect a function across the x-axis, then all of its values will be multiplied by negative one. So,  can be written in the following way:

Lastly, distribute the negative sign to arrive at the final answer.

It is important to follow the order of operations for this equation and find a solution that satisfies both F(x) and G(x).

Recall the order of operations is PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

The correct answer is 4 because 

F(x) = 2x + 3^x + (9x/3) = 2(4) + 3⁴ + ((9 * 4)/3) = 101, and

G(x) = (((2⁴ + 4⁴)/2) - 4 * 4) – 5(4) + 1 = 101.  

Define the variables x = first number and x + 2 = second number

The product is x(x + 2) = 15, so we need to solve the quadratic equation x² + 2x – 15 = 0.  Factoring we get (x + 5)(x – 3) = 0, so x = –5 or x = 3.  The problem calls for negative numbers, so the answers are –5 and –3 and the sum is –8

Factor the equation (4x – 1) (x + 1)

The solutions are x = –1 and x = 1/4.

The difference is (1/4) – (–1) = 5/4