Question

A friend looks at the graph of y=x? and observes that if you start at the origin, the graph increases whether you go to the right or the left, so the graph is increasing everywhere. Explain why this reasoning is incorrect. Choose the correct answer below O A. By the definition of an increasing function, a function is increasing if(x) > >) whenever , >xy When the friend looks at the graph to the left of this definition is broken. Thus, the function is not increasing everywhere O B. By the definition of an increasing function, a function is increasing if(x) >F(X) whenever xix. When the friend looks at the graph to the left of this definition is broken. Thus, the function is not increasing everywhere. OC By the definition of an increasing function, a function is increasing if(x) <(xs) whenever * When the trend looks at the graph to the left of this definition is broken. Thus, the function is not increasing everywhere. O D. By the definition of an increasing function, a function is increasing if(x) <f(x) whenever , when the friend looks at the graph to the left of this definition is broken. Thus, the function is not increasing everywhere.

Answer 1

The correct option is A.

An increasing function means that the value of that function f(x) will increase as x value increases. Put differently, for an increasing function, as we reduce value of x, the value of f(x) decreases too.

When we look to the left side of origin of y=x^2 function , as we move to the left , x value becomes more and more negative meaning x value reduces [ and does not increase] but we see f(x) value increases as we move to the left. This is not expected in an increasing function. At x=-1, f(x)=1; x=-2,f(x)=4 and so on .

Hope explanation is clear. Will appreciate feedback.