If the points (0, 0), (-1, 1), and (-2, 2) lie on the graph of function h, then which of the following rules could represent the function?
a. h(x) = x 2
b. h(x) = |x|
c. h(x) = -2x

We can plug in the values:
A ) 0 = 0² ,  1 = ( - 1 )²,   2 ≠ ( -2)²
B ) 0 = | 0 |,  1 = | -1 |,  2 = | - 2 |
C ) 0 = - 2 · 0,  1 ≠ - 2 · ( -1 ),  2 ≠ - 2 · ( - 2 )
B ) h ( x ) = | x |

Use photo math it

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

 

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.