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Solving equations by graphing functions
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Terms in this set (14)
Which of the following types of equations have you learned to solve using algebraic methods?
Quadratic
Exponential
Radical
Linear
Rational
(half right)
A solution of the equation ƒ(x ) = g(x ) is the same as (select all that apply)
The x-value of a solution to the system of equations y = ƒ(x ) and y = g(x ).
The x-coordinate of an intersection point of the graphs of y = ƒ(x ) and y = g(x ).
The y-coordinate of an intersection point of the graphs of y = ƒ(x ) and y = g(x ).
Use algebra to solve 3x + 4 = 1/x. The exact solutions are x =
-2±√7 / 3
(half right)
Find the exact solution(s) to the equation below by solving algebraically. Select all that apply.
8x^2-3=√16x+9
1, 1/2, -1/2
What are the solutions to the equation 4x 3 - 5x = |4x|? List your answers in increasing order.
0, 1.5, -0.5
Graph y = x 3 and y = 16/x on the same set of coordinate axes. Use the graphs to find the exact solutions to the equation x^3 =16/x . Verify by substitution that they satisfy the equation.
x= 2,-2
Graph y =√x + 2 and y = 3x on the same set of coordinate axes. Use the graphs to find the exact solutions to the equation √x + 2 = 3x. Then, find the solutions using an algebraic method.
Move all the terms to the left and set equal to zero. Then set each factor equal to zero. x=1
What are the solutions to the equation √5x+1 = x+1?
The solutions are x =
0
and
3
The following values represent exponential function ƒ(x) and linear function g(x).
ƒ(1) = 2 g(1) = 2.5
ƒ(2) = 6 g(2) = 4
A. Determine whether or not there is a solution to the equation In 2-3 sentences describe whether there is a solution to the equation ƒ(x)=g(x) between x=1 and x=2.
B. Use complete sentences to justify your claim.
a. no solution
I only got a half credit because I did not explain.
Use a graphing calculator or online application to find the solution to 3 -x = x 3 + x to the nearest tenth.
The solution is approximately x =
0.48
Use a graphing calculator or online application to find the solutions to x 2 - 9 = 6√3 / x to the nearest tenth.
The solution is approximately _____.
x = -1.7 and 3.5
Use a table of values to find the solution to the equation ƒ(x ) = h(x ) where f(x) = 1 / x+1 and h(x ) = 2x + 3.
Show your work
x= -0.5, -2
Solve by combining expressions and isolating the x variable.
Use the table and a calculator to help you find a solution to 0.1 • 2 x =4/x , rounded to the nearest whole number.
A solution to this equation to the nearest whole number is x = .
Does this equation have any other solutions?
4
no
The following values represent linear function ƒ(x) and rational function g(x).
ƒ(3) = 7 g(3) = 5.6
ƒ(4) = 5 g(4) = 6.7
A. Determine whether or not there is a solution to the equation In 2-3 sentences describe whether there is a solution to the equation ƒ(x)=g(x) between x=3 and x=4.
B. Use complete sentences to justify your claim.
As you can see, it's a decreasing continuous function (decreasing because f(4) < f(3) being because this is a linear function. Given g(x) is continuous in the range [3,4] if and only if m(x) doesn't equal 0 in the same range. Since we don't know if m(x) meets those requirements, we don't know if there is a solution to f(x)=g(x)
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