Ben and Carmella want to go to a basketball game. Carmella proposes they use a bag of 90 lettered tiles to decide who will pay f
or the tickets. Of the tiles, 35 are vowels and the rest are consonants. She will blindfold Ben and ask to him randomly choose a tile. If Ben picks a vowel, Carmella will pay for the tickets. If Ben picks a consonant, he will pay for the tickets.
Carmella distributes the 90 tiles into two boxes that are located to the left and to right of Ben. She tells Ben that there are a total of 43 lettered tiles in the box on his left, and 43 of the tiles in the box on his right are consonant tiles. Carmella gives Ben three options of how to select his tile.
Method 1: choose randomly from the box on his right
Method 2: choose randomly from the box on his left
Method 3: mix the letter tiles back together, and choose randomly from the entire set of tiles
Use this information to complete the statement.
The probability that Carmella will pay for the tickets is greatest, approximately __%, if Ben selects his tile using method __.
Carmella distributes the 90 tiles into two boxes that are located to the left and to right of Ben. She tells Ben that there are a total of 43 lettered tiles in the box on his left, and 43 of the tiles in the box on his right are consonant tiles. Carmella gives Ben three options of how to select his tile.
Method 1: choose randomly from the box on his right
Method 2: choose randomly from the box on his left
Method 3: mix the letter tiles back together, and choose randomly from the entire set of tiles
Use this information to complete the statement.
The probability that Carmella will pay for the tickets is greatest, approximately __%, if Ben selects his tile using method __.
2 answers:
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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:
