Some steps to rewrite the expression x3 − 4x + x2 − 4 as a product of three factors are shown below:
2 answers:
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Answer:
Center: (4,8)
Radius: 2.5
Equation:
Step-by-step explanation:
It was given that; the endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5).
Note that the longest chord is the diameter;
The midpoint of the ends of the diameter gives us the center;
Use the midpoint formula;
The center is at;
To find the radius, use the distance formula to find the distance from the center to one of the endpoints.
The distance formula is;
The equation of the circle in standard form is given by;
We substitute the center and the radius into the formula to get;
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:
