Question

1. graph each function as a vertical compression of its parent function. see example 3
2. ( g(x) = 0.25|x| )
3. ( g(x) = 3x^2 )
4. ( g(x) = 1.5|x| )
5. ( g(x) = 0.75x^2 )
6. use the graph of ( f(x) ) to graph ( y = f(x + 1) + 2 ). see example 4

graph of f is shown
what transformations of ( f(x) = x^2 ) are applied to the function ( g )? see example 5

1. ( g(x) = 2(x + 1)^2 )
2. ( g(x) = (x - 3)^2 + 5 )
3. ( g(x) = -x^2 - 6 )
4. ( g(x) = 4(x - 7)^2 - 9 )
5. the graph shows the height ( y ) in feet of a flying insect ( x ) seconds after taking off from the ground. write an equation that represents the height of the insect as a function of time. see example 6

graph of insects height is shown

Explanation:

Problem 24: $g(x) = 0.25|x|$

Step1: Identify parent function

Parent function: $f(x)=|x|$

Step2: Apply vertical compression

Vertical compression by factor $\frac{1}{4}$: $g(x)=\frac{1}{4}|x|$

Step1: Identify parent function

Parent function: $f(x)=x^2$

Step2: Apply vertical stretch

Vertical stretch by factor 3: $g(x)=3x^2$

Step1: Identify parent function

Parent function: $f(x)=|x|$

Step2: Apply vertical stretch

Vertical stretch by factor $\frac{3}{2}$: $g(x)=\frac{3}{2}|x|$

Answer:

Graph is a vertical compression of $y=|x|$ by factor $\frac{1}{4}$; key points: $(0,0), (4,1), (-4,1)$

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Problem 25: $g(x) = 3x^2$