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The graph is vertically stretched by a factor of 2 and translated 3 units right when it is transformed. Option A is correct.
<h3>What is transformation of a function?</h3>Transformation of a function is shifting the function from its original place in the graph.
Types of transformation-
- Horizontal shift- Let the parent function is f(x). Thus by replacing parent function with f(x-b) shifts the graph b units right and by replacing parent function with f(x+b) shifts the graph b units left.
- Vertical shift- Let the parent function is f(x). Thus by replacing parent function with f(x)-c shifts the graph c units down and by replacing parent function with f(x)+c shifts the graph c units up.
The given function is,
This function is changed to the function,
Here the 3 units is substrate in the function. Thus, it is shiftet 3 units right. The number 2 is multiplied in the function which vertically stretched the graph by a factor of 2.
Thus, the graph is vertically stretched by a factor of 2 and translated 3 units right when it is transformed. Option A is correct.
Learn more about the transformation of a function here;
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Answer:
μ = 5.068 oz
Step-by-step explanation:
Normal distribution formula to use the table attached
Z = (x - μ)/σ
where μ is mean, σ is standard deviation, Z is on x-axis and x is a desired point.
98% of 6-oz. cups will not overflow means that the area below the curve is equal to 0.49; note that the curve is symmetrical respect zero, so, 98% of the cases relied between the interval (μ - some value) and (μ + some value)].
From table attached, area = 0.49 when Z = 2.33. From data, σ = 0.4 oz and x = 6 oz (maximum capacity of the cup). Isolating x from the formula gives
Z = (x - μ)/σ
2.33 = (6 - μ)/0.4
μ = 6 - 2.33*0.4
μ = 5.068
This means that with a mean of 5 oz and a standard deviation of 0.4 oz, the machine will discharge a maximum of 6 oz in the 98% of the cases.
Answer:
f(4) = 85 1/3 or 85.333...
Step-by-step explanation:
To find f(4), you must substitute 4 in place of x whenever x appears:
f(x) = *
f(4) = *
Next, simplify the exponent:
f(4) = * 256
Finally, multiply:
f(4) = 85 1/3 or 85.333...