Exercise 108 Page 90

a To complete the table, we must substitute each value of x in the function and simplify the right-hand side to find its corresponding y-value.

|c|c|c| [-1em] x & x^2-6x+5 & y [0.3em] [-0.8em] - 1 & ( - 1)^2-6( - 1)+5 & 12 [0.5em] [-0.8em] 0 & 0^2-6( 0)+5 & 5 [0.5em] [-0.8em] 1 & 1^2-6( 1)+5 & 0 [0.5em] [-0.8em] 2 & 2^2-6( 2)+5 & - 3 [0.5em] [-0.8em] 3 & 3^2-6( 3)+5 & - 4 [0.5em] [-0.8em] 4 & 4^2-6( 4)+5 & - 3 [0.5em] [-0.8em] 5 & 5^2-6( 5)+5 & 0 [0.5em] We can plot these ordered pairs in a coordinate plane. Since the rule is a quadratic function, the corresponding graph will be a parabola.

The parabola is opening upwards and has a minimum at (3,-4). There are two x-intercepts at x=1 and x=5. The graph also has a y-intercept at y=5.

b If a relation is a function, each x should only correspond to one y-value. We can investigate this by performing a Vertical Line Test. If we draw a vertical line anywhere in the graph, it should only hit the graph once.

As we can see, the vertical line only hits the graph once. If we drew the line along any other value of x, we would see the same thing happening. Therefore, our relation has passed the vertical line test with flying colors, and is a function.

c A function's domain is the set of all possible values of x that can be substituted into the function and give an output. Since we can substitute any value of x into the function, the domain for this function is all real numbers.

Domain: All real numbers The range describes the corresponding y-values that the function can give. From the graph, we can see that the lowest possible value of y is -4. With this information, we can determine the range. Range: y ≥ -4

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Exercise 108 Page 90

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