A coordinate grid with 2 lines. The first line is labeled f(x) and passes through (negative 4, 3), (0, 3) and (4, 3). The second line is labeled g(x) and passes through the points (negative 2, negative 5), (0, negative 2), and (2, 1) Determine the input value for which the statement f(x) = g(x) is true. From the graph, the input value is approximately . f(x) = 3 and g(x) = x – 2 3 = x – 2 5 = x The x-value at which the two functions’ values are equal is .

explanation:

remove parenthesis:

=

apply rule

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multiply fractions:

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=

divide:

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mordancy.

60: 45 =12: 9 =4: 3 so the answer is 4: 3

x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81