Evaluate each function below. 52. If f(x) = 2x + 7, find f(8). 54. Find the range of the function f(x) = x^2 - 6x if the domain is { -7, -2, 1}. 55. Given the graph of f(x) below,... Evaluate each function below. 52. If f(x) = 2x + 7, find f(8). 54. Find the range of the function f(x) = x^2 - 6x if the domain is { -7, -2, 1}. 55. Given the graph of f(x) below, find f(2). Read more

Steps to Solve

1. Determine Domain and Range from Relations

For the sets of coordinates in each table or graph:

• Domain (D): List all unique x-values.
• Range (R): List all unique y-values.

For example, for coordinates (((2, 2), (-1, -1), (0, -1), (4, 2))):

• Domain: ( D = {2, -1, 0, 4} )
• Range: ( R = {2, -1} )

2. Check if Relation is a Function

A relation is a function if each input (x-value) corresponds to exactly one output (y-value).

• In the first set, there are unique x-values, so it is a function.
• In the second set, if any x-value repeats with a different y-value, it's not a function.

3. Evaluate the Function

For ( f(x) = 2x + 7 ):

• Substitute ( x = 8 ):

  $$ f(8) = 2(8) + 7 = 16 + 7 = 23 $$

4. Finding the Range for a Function

Given ( f(x) = x^2 - 6x ) with the domain ( { -7, -2, 1 } ):

• Calculate ( f(x) ) for each x-value:

  $$ f(-7) = (-7)^2 - 6(-7) = 49 + 42 = 91 $$
  $$ f(-2) = (-2)^2 - 6(-2) = 4 + 12 = 16 $$
  $$ f(1) = (1)^2 - 6(1) = 1 - 6 = -5 $$

Range is ( R = {91, 16, -5} ).

5. Finding the Value from the Graph

For the function based on the graph, to find ( f(2) ), locate where ( x = 2 ) on the graph and read the corresponding y-value.