Exponential Growth Homework Directions: Match each function with the correct graph.- _= 2(3)* = 1/₂(4)* _= 2(5)x = 5(4)x -Totatx) 12 m TOT ++/b6% Make a table from -2 to 2 and then make a sketch of each exponential growth function. f(x) = -4(2)* f(x) = (5)* €(x) d(x)

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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**Algebra 2/Precalc: Homework**

**Date:** 10/12  
**Period:** 2  

---

**Exponential Growth Homework**

**Directions:** Match each function with the correct graph.

1. ______ = 2(3)^x
2. ______ = 1/2(4)^x
3. ______ = 2(5)^x
4. ______ = 5(4)^x

(Graph has multiple curves labeled a(x), b(x), c(x), d(x). Each curve represents exponential growth functions with different base values.)

---

Make a table from -2 to 2 and then make a sketch of each exponential growth function.

f(x) = -4(2)^x  
f(x) = 1/2(5)^x

(Two empty grids are provided with axes labeled for plotting the functions.)
Transcribed Image Text:**Algebra 2/Precalc: Homework** **Date:** 10/12 **Period:** 2 --- **Exponential Growth Homework** **Directions:** Match each function with the correct graph. 1. ______ = 2(3)^x 2. ______ = 1/2(4)^x 3. ______ = 2(5)^x 4. ______ = 5(4)^x (Graph has multiple curves labeled a(x), b(x), c(x), d(x). Each curve represents exponential growth functions with different base values.) --- Make a table from -2 to 2 and then make a sketch of each exponential growth function. f(x) = -4(2)^x f(x) = 1/2(5)^x (Two empty grids are provided with axes labeled for plotting the functions.)
**Educational Website Content:**

Title: Graphing Exponential Functions Using the 3-Point Method

---

In today's lesson, you are asked to sketch graphs of exponential functions using the 3-point method. Below, you'll find the functions to be graphed, along with their respective coordinate grids.

1. **Function 1:** \( f(x) = 4 \left(\frac{5}{2}\right)^x \)

   - **Coordinate Grid**: The graph is to be plotted on a standard grid with x-axis and y-axis both ranging from -2 to 8. This is an exponential growth function. You should identify three key points (commonly where x is -1, 0, and 1) on the function, mark them on the grid, and sketch the exponential curve through these points.

2. **Function 2:** \( f(x) = \frac{3}{4} (6)^x \)

   - **Coordinate Grid**: Similar grid ranges apply here. This function represents exponential growth with a smaller base multiplier. Use the 3-point method to identify the values of the function when x takes on strategic values, plot them, and sketch the resulting curve.

3. **Function 3:** \( f(x) = -3(2)^x \)

   - **Coordinate Grid**: The graph area features negative y-values since it is a reflected exponential function due to the negative sign. Select your points where x takes values that will clearly demonstrate the function's downward trend (e.g., x = -1, 0, 1).

**Note**: Utilize grid lines to ensure precision and neatness in your sketches. The 3-point method will provide you with significant points to accurately reflect the behavior of each exponential function.

For further exploration, consider the transformations applied by the coefficients and bases in each function and how they affect the graph's shape and direction. 

Happy graphing!
Transcribed Image Text:**Educational Website Content:** Title: Graphing Exponential Functions Using the 3-Point Method --- In today's lesson, you are asked to sketch graphs of exponential functions using the 3-point method. Below, you'll find the functions to be graphed, along with their respective coordinate grids. 1. **Function 1:** \( f(x) = 4 \left(\frac{5}{2}\right)^x \) - **Coordinate Grid**: The graph is to be plotted on a standard grid with x-axis and y-axis both ranging from -2 to 8. This is an exponential growth function. You should identify three key points (commonly where x is -1, 0, and 1) on the function, mark them on the grid, and sketch the exponential curve through these points. 2. **Function 2:** \( f(x) = \frac{3}{4} (6)^x \) - **Coordinate Grid**: Similar grid ranges apply here. This function represents exponential growth with a smaller base multiplier. Use the 3-point method to identify the values of the function when x takes on strategic values, plot them, and sketch the resulting curve. 3. **Function 3:** \( f(x) = -3(2)^x \) - **Coordinate Grid**: The graph area features negative y-values since it is a reflected exponential function due to the negative sign. Select your points where x takes values that will clearly demonstrate the function's downward trend (e.g., x = -1, 0, 1). **Note**: Utilize grid lines to ensure precision and neatness in your sketches. The 3-point method will provide you with significant points to accurately reflect the behavior of each exponential function. For further exploration, consider the transformations applied by the coefficients and bases in each function and how they affect the graph's shape and direction. Happy graphing!
Expert Solution
Step 1

According to bartleby guidelines when student post multiple subpart question then expert must have to answer first three subpart.

 

Matching is very easy.

We just need to put x=0 in each function.

 

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