Nancy is checking to determine if the expressions x + 4 + x and 6 + 2 x minus 2 are equivalent. When x = 3, she correctly finds
that both expressions have a value of 10. When x = 5, she correctly evaluates the first expression to find that x + 4 + x =14. What is the value of the second expression when x = 5, and are the two expressions equivalent? The value of the second expression is 8, so the expressions are not equivalent. The value of the second expression is 14, so the expressions are equivalent. The value of the second expression is 16, so the expressions are equivalent. The value of the second expression is 18, so the expressions are not equivalent.
The average rate of change is also known as the slope. If we are looking to find the average rate of change between x = -1 and x = 2, in order to find the slope between those 2 x values, we need the y's that go along with them. Fill in -1 for x in the function and solve for y: . That means that the coordinate is (-1, 0). Fill in 2 for x in the function and solve for y: . The coordinate there is (2, -3). Now we can set up the slope formula to find the average rate of change between those 2 points: . Therefore, the average rate of change between x = -1 and x = 2 is -1