DETERMINE DOMAIN AND RANGE FROM ITS GRAPH

A number b is in the domain of a function f if and only if the line x = b intersects the graph of f.

A number c is in the range of a function f if and only if the horizontal line y = c intersects the graph of f .

Question 1 :

Find the domain of the function given below and estimate the value of f(3), where f is the function.

By drawing a vertical line on the graph, we may find the domain of the function.

The vertical line intersects the x-axis at the points 1 and 4.

So the domain is [1, 4]

Like that, by drawing a horizontal line, we get the range.

Hence the range of the given function is [-1, 3].

Question 2 :

Suppose f is the function with domain [1, 4] whose graph is shown here.

(a) Is 1.5 in the range of f ?

(b) Is 4 in the range of f ?

(c) Make a reasonable guess of the range of f .

Solution : 

In order to check if the given values is in range, we have to do horizontal line. The range of the given function is [-1, 3].

(i)  The value 1.5 lies on the interval. So 1.5 is in the range. 

(ii)  The value 4 does not lie on the given interval. Hence it is not in range.

(iii)  The range for the given function is [-1, 3]

Question 3 :

Shown below is the graph of a function f .

(a) What is the domain of f ?

(b) What is the range of f ?

By drawing vertical lines from the starting and ending point on the graph, we may find the domain.

In the same way, by drawing horizontal lines, we may get the range.

So the domain of the given function is [0, 4] and range is [-3, 1].

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