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Big Ideas Math Algebra 2, 2014

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Big Ideas Math Algebra 2, 2014 View details

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Exercise 1 Page 66

The graph of f(x) has been scaled horizontally. Use a point on the graph of g(x) to determine the horizontal scale.

To obtain g(x), we must translate the graph of f(x) 2 units up and then stretch it horizontally by a factor of 12.

Practice makes perfect

We are given the graphs of two functions, namely, f(x)=x^2 and g(x).

First, we see that the vertex of g(x) is 2 units above the vertex of f(x). We will start by translating the graph of f(x) up 2 units. h(x) = f(x) + 2

Now, let's plot g(x) and h(x) on the same coordinate plane and compare them.

We see that the graphs of g(x) and h(x) still do not match. However, we can see that the graph of g(x) is wider, which means that we have to make a horizontal stretch. In other words, g(x)= h( ax).

To figure out the scale factor, we will use the fact that g(2)=3. g(2)=3 ⇒ h( a* 2)=3 Next, we substitute h(x)=x^2+2 and solve the equation for a.

h(x)=x^2+2

x= a* 2

h( a* 2)=( a* 2)^2+2

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Solve for a

h( a* 2)= 3

3 = ( a* 2)^2+2

Calculate power

3 = 4 a^2+2

LHS-2=RHS-2

1 = 4 a^2

.LHS /4.=.RHS /4.

1/4 = a^2

sqrt(LHS)=sqrt(RHS)

± sqrt(1/4) = a

Calculate root

± 1/2 = a

Rearrange equation

a = ± 1/2

Since a must be positive, we will discard the negative option. Now, we are ready to write our function g(x) in terms of f(x). g(x) &= h( 1/2x) &= f( 1/2x) + 2 In conclusion, to obtain g(x) we must translate the graph of f(x) 2 units up and then stretch it horizontally by a factor of 12.

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Exercises p.66