Exercise 4 Page 543

Practice makes perfect

a Consider the given function.

g(x)=sqrt(x-1) Let's write a table of values for this function. Since the radicand cannot be negative, we will start with x=1.

We will now plot the points and connect them with a smooth curve.

Next, we will compare this graph to the square root function.

We can see that the graph of g(x) is a translation of f(x) by one unit to the right.

b Consider the given function.

g(x)sqrt(x)-1 Let's write a table of values for this function. Since the radicand cannot be negative we will start from x=0.

We will now plot the points and connect them with a smooth curve.

Next, we will compare this graph to the square root function.

We can see that the graph of g(x) is a translation of f(x) by one unit down.

c Consider the given function.

g(x)=2sqrt(x) Let's write a table of values for this function. Since the radicand cannot be negative we will start from x=0.

We will now plot the points and connect them with a smooth curve.

Next, we will compare this graph to the square root function.

We can see that the graph of g(x) is a vertical stretch of f(x) by a factor of 2.

d Consider the given function.

g(x)=-2sqrt(x) Let's write a table of values for this function. Since the radicand cannot be negative we will start from x=0.

We will now plot the points and connect them with a smooth curve.

Next, we will compare this graph to the square root function.

We can see that the graph of g(x) is a composite transformation. It is an x-axis reflection of a vertical stretch of f(x) by a factor of 2.

Communicate Your Answer p.543

Monitoring Progress p.544-547

Exercises p.548-550

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