Leslie analyzed the graph to determine if the function it represents is linear or non-linear. First she found three points on the graph to be open paren negative 1 comma negative 4 close paren , open paren 0 comma negative 3 close paren , and open paren 2 comma 5 close paren Next, she determined the rate of change between the points open paren negative 1 comma negative 4 close paren and open paren 0 comma negative 3 close paren to be the fraction with numerator negative 3 minus negative 4 and denominator 0 minus negative 1 is equal to 1 over 1 is equal to 1 and the rate of change between the points open paren 0 comma negative 3 close paren and open paren 2 comma 5 close paren to be the fraction with numerator 5 minus negative 3 and denominator 2 minus 0 is equal to 8 halves is equal to 4 Finally, she concluded that since the rate of change is not constant, the function must be linear. Why is Leslie wrong?
Answer
A
The expressions the fraction with numerator negative 3 minus negative 4 and denominator 0 minus negative 1 and the fraction with numerator negative 3 minus negative 5 and denominator 2 minus 0 both equal 1 .
B
She miscalculated the rates of change.
C
Her conclusion is wrong. If the rate of change is not constant, then the function cannot be linear.
D
The points open paren negative 1 comma negative 4 close paren , open paren 0 comma negative 3 close paren , and open paren 2 comma 5 close paren are not all on the graph.