Explain why the x-coordinates of the points where the graphs of y = f(x) and y = g(x) intersect are the solutions of f(x) = g(x); find the solutions approximately using technology. Include cases where f(x) and/or g(x) are polynomial rational exponential logarithmic and trigonometric functions.

Sample Practice Questions (3)

How many real solutions exist for the equation

\frac{2}{x} = x + 1

Multiple choice · diagramSee Answer + Explanation →

Consider the functions

f (x) = 2^{x}

and

g (x) = x + 2

. Using a graphing calculator, what are the approximate x-coordinates of the points where

f (x) = g (x)

? Round your answers to the nearest hundredth.

x \approx - 2.00

and

x \approx 0.00

x \approx - 1.69

and

x \approx 2.00

x \approx 0.00

and

x \approx 1.00

x \approx - 1.00

and

x \approx 3.00

Multiple choice · diagramSee Answer + Explanation →

Graph the functions

f (x) = ∣ x - 2∣ + 1

and

g (x) = - x + 5

on the same coordinate plane. Then, use your graph to find the approximate x-coordinates of the points of intersection. Round your answers to the nearest tenth.

Open response · diagramSee Answer + Explanation →

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More Algebra II Standards

NY-A.SSE.2-AIIUse the structure of an expression to identify ways to rewrite it. Apply to polynomial and rational expressions in the context of Algebra II.→NY-A.SSE.4Derive the formula for the sum of a finite geometric series and use the formula to solve problems.→NY-A.APR.2Know and apply the Remainder Theorem: for a polynomial p(x) and a number a the remainder on division by x - a is p(a). If p(a) = 0 then (x - a) is a factor of p(x).→NY-A.APR.3Identify zeros of polynomials when suitable factorizations are available and use the zeros to construct a rough graph of the function defined by the polynomial.→

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