Exercise 3 Page 3

Practice makes perfect

a In Exploration I, we have been given the graphs of eight basic parent functions. By classifying each function, we will write an equation for each of them. Let's begin with the first graph.

The graph has a distinct

V -

shape, which tells us that it is a graph of an absolute value function. Since it is a parent function graph, its equation can be written as follows.

f (x) = ∣ x ∣

Now, we will check whether our equation is correct by using a graphing calculator. To draw a graph on a calculator, we first press the

Y =

button and type the equation in one of the rows. Having written the function, we can push

GRAPH

to draw it.

Because the graph of our equation matches the given graph, our equation is correct.

b In the second graph, we can see that the domain and range of the function are all positive real numbers.

The function that satisfies these domain and range is a square root function. Let's write its equation!

f (x) = x

Now, we will verify that our equation is correct.

As we can see, our graph is the same as the given one, so our equation is correct.

c Notice that the graph is a straight line whose slope is

0 .

Therefore, it is the graph of the parent function of a constant function.

f (x) = 1

Let's check it!

Since the above graph matches the given graph, our equation is correct.

d The graph intersects the

y -

axis at

(0, 1) .

Additionally, its domain is the set of all real numbers and its range is the set of all positive real numbers.

Thus, it is the graph of the parent function of an exponential function. The general equation of it can be written as follows.

f (x) = b^{x}, where b > 0 and b \neq = 1

Looking at the graph, we can see that

y = 2

when

x = 1 .

Therefore, we can conclude that

b = 2

for the given graph.

f (x) = 2^{x}

Now, we can check whether our equation is correct.

The graph matches the given one, so the equation is correct.

e Let's continue with the fifth graph.

As we can see, the graph has an

S -

shape. Therefore, it is the graph of the parent function of a cubic function and its equation can be written as follows.

f (x) = x^{3}

Now, we will verify our equation.

With this graph, we can tell that the equation is correct.

f The next graph is a straight line with a slope different than

0 .

This means that it is a linear function, and the parent function of a linear function is the following.

f (x) = x

Let's check it by using a graphing calculator.

As we can see, it matches the given graph.

g This graph is made up of two branches and asymptotes.

Therefore, it is the graph of the parent function of a reciprocal function. Its equation can be written as follows.

f (x) = \frac{1}{x}

Let's verify that our equation is correct.

We got the same graph as the given one, so our equation is correct.

h Finally, we will examine the last graph.

Since it is a parabola, we can conclude that it is the graph of the parent function of a quadratic function.

f (x) = x^{2}

By using a graphing calculator, we will again verify whether the above equation is correct.

As a result, our equation is correct.

Subchapter links

Communicate Your Answer p.3

Monitoring Progress p.4-7

Exercises p.8-10

Exercise 3 Page 3

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