Mod 9 Part 2 Test Review

Given the original exponential function defined by y=4^x, how would the graph change if the function were:

y=2(4)^x-3+1?

• Vertically stretched by a factor of 2, right 3, and up 1

• Vertically compressed by a factor of 1/2, left 3 and down 1

• Vertically compressed by a factor of 1/2, right 3, and down 1

• Vertically stretched by a factor of 2, left 3, and up 1

Answer explanation

The function y=2(4)^(x-3)+1 is a transformation of y=4^x. It is vertically stretched by a factor of 2 (the coefficient 2), shifted right 3 (the x-3), and shifted up 1 (the +1). Thus, the correct choice is: Vertically stretched by a factor of 2, right 3, and up 1.

• Horizontal shift

• Vertical Translation

• Reflection over the x-axis

• Reflection over the y-axis

Answer explanation

Adding a constant "k" to the function y=a(b)^x+k results in a vertical translation of the graph. This means the entire graph shifts up or down by the value of "k", without affecting its shape or orientation.

What equation would yield a transformation right 3 units if your initial function was y=2^x

• y=2^x-3

• y=2^x+3

• y=2^x+3

• y=2^x-3

Answer explanation

To shift the function y=2^x right by 3 units, we replace x with (x-3). Thus, the correct transformation is y=2^(x-3). This matches the choice y=2^(x-3), which is the correct answer.

Compare f(x) = 3^x- 4 with the basic function g(x) = 3^x

• 4 units up

• 4 units to the left

• 4 units to the right

• 4 units down

Answer explanation

The function f(x) = 3^x - 4 is a vertical shift of g(x) = 3^x. The '-4' indicates that the graph of f(x) is shifted 4 units down from g(x). Thus, the correct answer is 4 units down.

What is the transformation?

• Horizontal Translation left 2

• Vertical Translation down 2

• None

• Reflection across the line y=0

Answer explanation

The correct transformation is a reflection across the line y=0, which flips points over the x-axis. This means that for any point (x, y), it becomes (x, -y), indicating a vertical flip.

What transformations have happened to f(x) = 2^x if the new equation is
 g(x) = -2^(x+3) -6

• It stayed the same

• reflects, up 3, left 6

• reflects, right 3, down 6

• reflects, left 3, down 6

Answer explanation

The transformation from f(x) = 2^x to g(x) = -2^(x+3) - 6 involves a reflection across the x-axis (the negative sign), a left shift of 3 units (x+3), and a downward shift of 6 units. Thus, the correct choice is reflects, left 3, down 6.

What transformations occur in the following function?

• right 3, up 2

• left 3, up 2

• left 3, down 2

• right 3, down 2

Answer explanation

The function is transformed by moving right 3 units and up 2 units. This means the graph shifts horizontally to the right and vertically upwards, confirming the correct choice is 'right 3, up 2'.

• Translates left 2 units

• Translates right 2 units

• Translates up 2 units 

• Translates down 2 units

Answer explanation

The function g(x) = 3^(x+2) can be rewritten as g(x) = 3^x * 3^2. The +2 in the exponent indicates a horizontal shift. Therefore, f(x) = 3^x is translated left by 2 units to obtain g(x).

• Vertical Stretch

• Vertical Compression

• Translation up 5 units

• Reflection across the x-axis

Answer explanation

The function g(x) = 5(3^x) represents a vertical stretch of the parent function f(x) = 3^x by a factor of 5. This means that the output values of g(x) are 5 times those of f(x) for the same x.

• Shifted up 5

• Shifted down 5

• Reflection over the x-axis

• Reflection over the y-axis

Answer explanation

The function g(x) = 7(3)^x - 5 is derived from f(x) = 7(3)^x by subtracting 5. This transformation shifts the graph down by 5 units, making 'Shifted down 5' the correct choice.