Question

use the given graph to determine if there are any solutions to the equation \\(-(5)^{3-x} + 4 = -2x\\).

• the solution is approximately 1.7 because it is the \\(x\\)-value of the intersection of the functions.
• the solution is approximately \\(-3.5\\) because it is the \\(y\\)-value of the intersection of the functions.
• there is no solution to the equation.
• the two solutions to the equation are 1.7 and \\(-3.5\\) because that is the intersection of the functions.

Explanation:

Identify the graphical representation of the equation

Using the Solving Exponential Equations Graphically knowledge point

$$
LATEXBLOCK0
$$

Find the intersection point of the two graphs

Using the Solving Exponential Equations Graphically knowledge point

$$ \text{Intersection Point} = (1.7, -3.5) $$

Determine the solution to the equation

Using the Solving Exponential Equations Graphically knowledge point

$$
LATEXBLOCK1
$$

Answer:

• (A) The solution is approximately 1.7 because it is the x-value of the intersection of the functions. (Correct answer)
• (B) The solution is approximately -3.5 because it is the y-value of the intersection of the functions.
• (C) There is no solution to the equation.
• (D) The two solutions to the equation are 1.7 and -3.5 because that is the intersection of the functions.