Solving equations by graphing functions
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
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.
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
Use algebra to solve 3x + 4 = 1/x. The exact solutions are x =
-2±√7 / 3
What are the solutions to the equation 4x 3 - 5x = |4x|? List your answers in increasing order.
0, 1.5, -0.5
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
(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
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)
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
Which of the following types of equations have you learned to solve using algebraic methods?
Quadratic Exponential Radical Linear Rational
What are the solutions to the equation √5x+1 = x+1?
The solutions are x = 0 and 3
(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 ).
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.