The domain of the sum of two functions is the intersections of the domains of the individual functions. Both and are square root functions, so their radicands must both be positive.

The domain of is the set of all values of such that:

Adding 8 to both sides:

This domain is .

The domain of  is the set of all values of such that:

Subtracting 8 tfrom both sides:

This domain is

The domain of is the intersection of the domains, which is .

The domain of the composition of functions is the set of all values  that fall in the domain of such that falls in the domain of .

, a polynomial function, so the domain of is equal to the set of all real numbers, . Therefore, places no restrictions on the domain of .

, a square root function, whose domain is the set of all values of that make the radicand nonnegative. Since the radicand is itself, the domain of  is simply the set of all nonnegative numbers, or . Therefore, we must select the set of all in such that , or, equivalently,

However, , so , with equality only if . Therefore, the domain of is the single-element set , which is not among the choices.

The domain of the difference of two functions is the intersections of the domains of the individual functions. Both and are square root functions, so their radicands must both be positive.

The domain of is the set of all values of such that:

Subtracting 8 tfrom both sides:

This domain is

The domain of  is the set of all values of such that:

Adding to both sides:

, or

This domain is .

The domain of  is the intersection of these, .

The range of a function is the set of all possible values of over its domain.

Since this function is piecewise-defined, it is necessary to examine both parts of the function and extract the range of each.

For , it holds that , so

,

or

.

For , it holds that , so

,

or

The overall range of is the union of these sets, or .

The price of the dish is a function of a single variable, the cost of the ingredients. One way to conceptualize the problem is by thinking of it in function notation. Let  be the variable representing the cost of the ingredients. Let  be a function of the cost of ingredients giving the price of the dish. Then, we can turn

"Price = (Cost of Ingredients) + (40% of the Cost of Ingredients) + 5"

into a regular equation with recognizable parts. Replace "Price" with  and replace "cost of ingredients" with the variable .

Simplify by combining like terms ( and ) to obtain:

The cost of ingredients for the steak dish is $14, so substitute 14 for .

All that's left is to compute the answer:

So, the steak dish will have a price of $24.60.

The power of  and  are both 1, so this is a linear equation of order 1. Therefore, the graph must be a straight line. We can eliminate A and E, since neither are straight lines. 

The equation is given in the slope-intercept form, , where  stands for the slope of the line and  stands for the line's y-intercept. Since , the coefficient of x, is positive here, we are looking for a line that goes upwards. We can eliminate D since it goes downwards, and therefore has a negative slope.

In the given equation, the constant , which represents the y-intercept, is also positive. Therefore, the line we are looking for also must intersect the y-axis at a positive value. The graph C appears to intersect the y-axis at a negative value, whereas the graph B appears to intersect the y-axis at a positive value. Therefore, B is the corresponding graph.

It is not necessary to actually find the solutions to a quadratic equation to determine the sum of its solutions.

First, get the equation in standard form by subtracting from both sides:

If a quadratic equation has two distinct solutions, which we are given here, their sum is the linear coefficient . In this problem, , making the correct choice.

The Intermediate Value Theorem (IVT) states that if the graph of a function is continuous on an interval , and and differ in sign, then has a zero on . Consequently, the way to answer this question is to determine the signs of on the endpoints of the subintervals - . We can do this by substituting each value for  as follows:

assumes positive values for and negative values for . By the IVT,  has a zero on .

Use the zeroes of the graph to determine the matching function. Zeroes are values of x where . In other words, they are points on the graph where the curve touches zero. 

Visually, you can see that the curve crosses the x-axis when , , and . Therefore, you need to look for a function that will equal zero at these x values. 

A function with a factor of  will equal zero when  , because the factor of  will equal zero. The matching factors for the other two zeroes,  and , are  and , respectively.  

The answer choice  has all of these factors, but it is not the answer because it has an additional zero that would be visible on the graph. Notice it has a factor of , which results in a zero at . This additional zero that isn't present in the graph indicates that this cannot be matching function.  

 is the answer because it has all of the required factors and, as a result, the required zeroes, while not having additional zeroes. Notice that the constant coefficient of negative 2 does not affect where the zeroes are.