Semester 1 EXAM

Front

Which graph represents a function?

Back

A function is a relation where each input has exactly one output. Graphically, this can be determined using the vertical line test.

Front

What is a flat rate in a pricing model?

Back

A flat rate is a fixed charge for a service, regardless of the amount used or consumed.

Front

How do you calculate the cost for a variable weight service?

Back

Cost = Flat Rate + (Cost per pound * Weight of garbage).

Front

Given f(x) = x^2 + 3x + 1, find f(-4).

Back

f(-4) = (-4)^2 + 3(-4) + 1 = 16 - 12 + 1 = 5.

Front

What is function composition?

Back

Function composition is the process of applying one function to the results of another function, denoted as (f(g(x))).

Front

Given f(x) = 2x and g(x) = x^2 + 3, find f(g(x)).

Back

f(g(x)) = f(x^2 + 3) = 2(x^2 + 3) = 2x^2 + 6.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. Solutions are the values that satisfy all equations simultaneously.

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

What is the solution to the system: 3x + 2y = 16 and 7x + y = 19?

Back

The solution is (2, 5).

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If a vertical line intersects the curve at more than one point, it is not a function.