Test B review, no calculators please help

Question

Answer 1

24).

The function .

Differentiate the function with respect to x.

.

Apply quotient rule of derivative : .

Apply power rule of differentiation : .

.

Solution : Option (a) is the correct choice.

Answer 2

23).

The graph represents a ratioanal function, because there is a vertical asymptotes and the Horizontal or Oblique Asymptote.

So, the function may be y = 1/x or y = 1/x² or y = 1/x³.

Observe the graph, the domain of the function is set of all rean numbers x except 0.

And the graph has no y - intercept, because x can never equals to 0.

The graph has no x - intercept.

Therefore, the graph will not cross or touch either of the coordinate axes.

The range of the function(y = 1/x²) is +∞, and the range of the function(y = 1/x and y = 1/x³) is [+∞, - ∞].

So, the given graph represents a ratioanal function, i.e : y = 1/x².

Solution : Option (c) is the correct choice.