1. Introduction to Functions Honors Math – Grade 8

2. KEY CONCEPT Function A function is a relation in which each element of the domain is paired with exactly one element in the range. The table shows barometric pressures and temperatures recorded by the National Climate Data Center over a three-day period. Notice that when the pressure is 995 and 1006 millibars, there is more than one value for the temperature. This relation is not a function.

3. Determine whether each relation is a function. Explain. For each element of the domain (x), there is only one corresponding element in the range. This mapping DOES REPRESENT A FUNCTION. It does not matter if two elements of the domain are paired with the same element in the range. Look at the elements in x. The element 2 is paired with both 5 and 4. This relation DOES NOT REPRESENT A FUNCTION. {(-2, 4), (1,5), (3,6), (5,8), (7,10)} Look at the x-values. -2, 1, 3, 5, 7 Each element appears once. This relation IS A FUNCTION.

4. A vertical line can be used to determine if a graph of a relation is a function. KEY CONCEPT The Vertical Line Test The Vertical Line Test… 1.If a vertical line intersects a graph at two or more points, the graph is not a function. 2.If the vertical line intersects a graph only once, the graph is a function. FUNCTION NOT A FUNCTION FUNCTION

5. Determine whether each relation is a function. Use the Vertical Line Test. The vertical line intersects the graph at two or more points. This relation is not a function. Use the Vertical Line Test. The vertical line intersects the graph at two or more points. This relation is not a function. Use the Vertical Line Test. The vertical line intersects the graph only once. This relation is a function.

6. Equations that are functions can be written in a form called function notation. EquationFunction Notation In a function, x represents the independent quantity, or the elements of the domain and f(x) represents the dependent quantity, or the elements of the range. Read as “f of x.” For example, f(5) is the element in the range that corresponds to the element 5 in the domain. We say that f(5) is the function value of f when x = 5.

7. Find each function value. f(x) = 2x + 5 1. f(-2) Replace x with -2. Evaluate. 2. f(1) + 4 Replace x with -2. Evaluate. 3. f(3) Replace x with 3. Evaluate. 4. 2 – f(0) Replace x with 0. Evaluate.

8. Find each function value. f(t) = 2t 3 1. f(4) Replace t with 4. Evaluate. 2. 3[f(3)] Read as “3 times the f of 3.” First evaluate the f(3) then multiply the answer by 3.

9. The function h(t) = -16t 2 + 68t + 2 represents the height h(t) of a football in feet t seconds after it is kicked. 1. Find h(4) Replace t with 4. Evaluate. Use the Order of Operations. 2. Find 2[h(g)] Replace t with g. Simplify. Simplify again using the Distributive Property.