Math12 1 Transformations 1

This quiz covers topics on translations, reflections, expansions, and compressions.
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1.

Describe the changes from f(x):
2.

Describe the changes from f(x): y= 2f(2x+4)-5
3.

Write the f(x) equation for the following transformation: Horizontal compression by 1/4, horizontal translation left 1, vertical translation down 2 and vertical expansion by 2.
4.

The following graph is transformation of . What is the equation of the graph shown? (use sqrt(x) to represent )
5.

The polynomial function P(x) = x(x+1)(x+2) has three zeros: 0, -1, -2. What are the zeros of y= -2P(x)?
- A.
  
  0, 2, 4
- B.
  
  0, 1/2, 1
- C.
  
  0, -2, -4
- D.
  
  0, -1, -2
Correct Answer
D. 0, -1, -2

Explanation
The zeros of a polynomial function are the values of x for which the function equals zero. In this case, the polynomial function P(x) = x(x+1)(x+2) has zeros at x = 0, x = -1, and x = -2. When we multiply the function by -2, the zeros remain the same. Therefore, the zeros of y = -2P(x) are also 0, -1, and -2.

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6.

The polynomial function P(x) = x(x+1)(x+2) has three zeros: 0, -1, -2. What are the zeros of ?
- A.
  
  0, -1, -2
- B.
  
  0, -4, -8
- C.
  
  0, -1/4, -1/2
- D.
  
  0, 1, 2
Correct Answer
B. 0, -4, -8

Explanation
The given polynomial function P(x) = x(x+1)(x+2) has three zeros: 0, -1, and -2. The zeros of a polynomial are the values of x for which the function equals zero. In this case, when x = 0, x+1 = 0, and x+2 = 0, the function equals zero. Therefore, the zeros of the function are 0, -1, and -2. The answer choice 0, -4, -8 does not match the zeros of the function, so it is not correct. The answer choice 0, -1/4, -1/2 also does not match the zeros of the function. The answer choice 0, 1, 2 also does not match the zeros of the function.

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7.

If (8,-6) is a point on the graph of y=f(x), what must be the point on the graph of y= -f(2x)+3? (write your answer in the form of (x,y))

Correct Answer
(4,9)

Explanation
If (8,-6) is a point on the graph of y=f(x), it means that when x=8, y=-6.
To find the point on the graph of y= -f(2x)+3, we need to substitute x=4 into the equation.
When x=4, 2x=8, so we can use the point (8,-6) on the graph of y=f(x).
Plugging in 8 for x, we get y= -f(8)+3. Since y=-6 when x=8, we have y= -(-6)+3=9.
Therefore, the point on the graph of y= -f(2x)+3 is (4,9).

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8.

Given , write an equation for y= -f(x). (Express as x^3)
9.

Given , write an equation for y= f(-x). (Express as x^3)
10.

The function is reflected in the y-axis. What is the resulting, fully simplified, equation? (Express exponents with '^', for example = x^2

Math12 1 Transformations 1

Describe the changes from f(x):

Describe the changes from f(x): y= 2f(2x+4)-5

Write the f(x) equation for the following transformation: Horizontal compression by 1/4, horizontal translation left 1, vertical translation down 2 and vertical expansion by 2.

The following graph is transformation of . What is the equation of the graph shown? (use sqrt(x) to represent )

The polynomial function P(x) = x(x+1)(x+2) has three zeros: 0, -1, -2. What are the zeros of y= -2P(x)?

The polynomial function P(x) = x(x+1)(x+2) has three zeros: 0, -1, -2. What are the zeros of ?

If (8,-6) is a point on the graph of y=f(x), what must be the point on the graph of y= -f(2x)+3? (write your answer in the form of (x,y))

Given , write an equation for y= -f(x). (Express as x^3)

Given , write an equation for y= f(-x). (Express as x^3)

The function is reflected in the y-axis. What is the resulting, fully simplified, equation? (Express exponents with '^', for example = x^2