Math: b988eeec

ID: b988eeec 

(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Algebra)

Comment: Algebra meets a definition in this straightforward question.

Method 1: Since h(x) is generated from the sum of f(x) and g(x), it makes sense to start with that sum. To be honest, I would probably write down the third step only, since the arithmetic is not too involved. That is, we are only tracking two values that sum to give us the coefficient of x and another two values to give us the other number, and neither of these sums involves large numbers or even fractions with different denominators, so solving is streamlined.

h(x) = ((1/4)x - 9) + ((3/4)x + 21)

h(x) = (4/4)x + 12

h(x) = x + 12

Now, the x-intercept is where, in a graph, y = 0. That might seem backwards, but most people are comfortable with the y-intercept marking the point at which x = 0, so this is just the opposite relationship. Substitute this value for h(x) and solve.

(0) = x + 12

x = -12

The answer must be -12.

Method 2: Use the calculator portion of Desmos to add the fractions and the integers if you want to ensure you do not make any mistakes. Then, graph the function h(x).

The x-intercept is clearly (-12, 0), so the answer must be -12.

Method 3: Apart from working out each step in the first method above, I do not see how a separate method would be worth pursuing for this particular problem. It is one that will either take you a long time because the concept is murky or will take about 30 seconds, maybe a minute if you let the calculator do the work.