Question

Match the key feature of the graph with correct function by dragging the feature into the correct column.

1. F(x)= logv3 x
2. g(x) = 3^x

A. Has the x-intercept (1,0)
B. Has the Y-intercept (0,1)
C. Contains the point (1,3)
D. Contains the point (3,1)
E. Has a horizontal asymptote at y = 0 (the x-axis)
F. Has a verticak asymptote at x=0 (the y-axis

Answer 1

Let's analyze the functions and match them with their corresponding key features.

1. **f(x) = log₃(x)**
- A. **Has the x-intercept (1,0)**: Correct. The logarithm function has an x-intercept at (1,0), because log₃(1) = 0.
- B. **Has the Y-intercept (0,1)**: Incorrect. The logarithm function does not cross the y-axis.
- C. **Contains the point (1,3)**: Incorrect. log₃(1) = 0.
- D. **Contains the point (3,1)**: Correct. log₃(3) = 1.
- E. **Has a horizontal asymptote at y = 0 (the x-axis)**: Incorrect. The logarithm does not have a horizontal asymptote.
- F. **Has a vertical asymptote at x = 0 (the y-axis)**: Correct. The logarithm approaches negative infinity as x approaches 0 from the right.

2. **g(x) = 3^x**
- A. **Has the x-intercept (1,0)**: Incorrect. The exponential function does not have an x-intercept.
- B. **Has the Y-intercept (0,1)**: Correct. The exponential function has a y-intercept at (0, 1) because 3^0 = 1.
- C. **Contains the point (1,3)**: Correct. g(1) = 3^1 = 3.
- D. **Contains the point (3,1)**: Incorrect. g(3) = 3^3 = 27, not 1.
- E. **Has a horizontal asymptote at y = 0 (the x-axis)**: Correct. The exponential function approaches 0 as x approaches negative infinity.
- F. **Has a vertical asymptote at x = 0 (the y-axis)**: Incorrect. The exponential function does not have a vertical asymptote.

Now we can organize the features into the columns for each function:

**f(x) = log₃(x)**:
- A. Has the x-intercept (1,0)
- D. Contains the point (3,1)
- F. Has a vertical asymptote at x=0 (the y-axis)

**g(x) = 3^x**:
- B. Has the Y-intercept (0,1)
- C. Contains the point (1,3)
- E. Has a horizontal asymptote at y = 0 (the x-axis)