Gianna had $4.75 and Moriah had $6.42. They put their money together to buy party favors that cost $0.40 each.
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Answer:
3.58
Step-by-step explanation:
Given :
y = 2x + 4 -------- eq1
y = 2x - 4 -------- eq2
sanity check : both equations have same slope, so we can conclude that they are both parallel to one another.
Step 1: consider equation 1, pick any random x-value and find they corresponding y-value. we pick x = -2
This gives us y = 2(-2) + 4 = 0
Hence we get a point (x,y) = (-2,0)
Step 2: express equation 2 in general form (i.e Ax + By + C = 0)
y = 2x-4 -------rearrange---> 2x - y -4 = 0
Comparing with the general form, we get A = 2, B = -1, C = -4
Recall that the distance between 2 parallel lines is given by the attached formula (see attached picture).
substituting the values for A, B, C and (x, y) from the previous step:
d = | (2)(-2) + (-1)(0) + (-4) | / √(2² + (-1)²)
d = | -4 + 0 - 4 | / √(4 + 1)
d = | -8 | / √5
d = 8 / √5
d = 3.5777
d = 3.58 (rounded 2 dec. pl)
Function transformation involves changing the form of a function
- The transformation from f(x) to g(x) is a horizontal shift 3 units left, followed by a vertical stretch by a factor of 4
- The x and y intercepts are -0.67 and 1.91, respectively.
- The behavior of g(x) is that, g(x) approaches infinity, as x approaches infinity.
The functions are given as:
<u>(a) The transformation from f(x) to g(x)</u>
First, f(x) is shifted left by 1 unit.
The rule of this transformation is:
So, we have:
Next. f'(x) is vertically stretched by a factor of 4.
The rule of this transformation is:
So, we have:
Hence, the transformation from f(x) to g(x) is a horizontal shift 3 units left, followed by a vertical stretch by a factor of 4
<u>(b) Sketch of g(x)</u>
See attachment
<u>(c) Asymptotes</u>
The graphs of g(x) have no asymptote
<u>(d) The intercepts, and the behavior of f(x)</u>
The graph crosses the x-axis at x =-0.67, and it crosses the y-axis at y = 1.91
Hence, the x and y intercepts are -0.67 and 1.91, respectively.
The behavior of g(x) is that, g(x) approaches infinity, as x approaches infinity.
We know this because, the value of the function increases as x increases
Read more about function transformations at:
