Part a: The value of y is 11 for x = 2.
Part b: The graph for the function y = x² + 4x -1 is drawn.
Part c: Range; (-∞,-3.75]∪[-0.25,∞)
Part d: The function is y = -5 - (x + 2)².
Part e: The approximate value of √3 is 1.732.
<h3>What is defined as the term function?</h3>
- A function is an expression, rule, or law in mathematics that defines a relationship between one dependent variable (a independent variable) and also one more variable (the dependent variable).
- Functions are common in mathematics and are required for the formulation of actual relationships with in sciences.
For the given function;
y = x² + 4x -1, the values of y for the corresponding x is given in tables shown.
Part a: value of y when x = 2.
Put x = 2 in the function;
y = x² + 4x -1
y = 2² + 4×2 -1
y = 11
The value of y is 11 for x = 2.
Part b: The graph for the function y = x² + 4x -1 is drawn using the scale of 10 small divisions as 1 unit along x and y axis.
Part c: Range of value of x for which y ≥ -2.
Locate the point of x from the graph for which the value of y y ≥ -2.
Range; (-∞,-3.75]∪[-0.25,∞)
Part d: The function in the form of y = k - (x - h)², where k and h are the vertex.
The vertex from the graph is found as (-2, -5) (h, k)
Putt in the equation;
y = k - (x - h)²
y = -5 - (x - (-2))²
y = -5 - (x + 2)²
Part e: 2 - √3 is the root of the equation 0 = x² + 4x -1.
It 2 - √3 is the root of the equation, then by putting this value at x the equation becomes zero.
The approximate value of √3 is 1.732 which is found by long division method.
To know more about the function, here
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