Question

6. write the equation of a logarithmic function that has been vertically stretched by 4, reflected in the x-axis, horizontally compressed by 1/9, moved 11 units up and 12 units left. justify your answer.

Answer 1

To write the equation of a transformed logarithmic function, use the general form y = a * log(base b)(x - h) + k and determine the values of a, b, h, and k based on the given transformations.

Step-by-step explanation:

To write the equation of a logarithmic function that has been vertically stretched by 4, reflected in the x-axis, horizontally compressed by 1/9, moved 11 units up, and 12 units left, we can start with the general form of a logarithmic function: y = a * log(base b)(x - h) + k.

Here's how we can determine the values of a, b, h, and k based on the given transformations:

Vertical stretch by 4: This corresponds to the value of a, which is 4.

Reflection in the x-axis: This changes the sign of the entire function, so a becomes -4.

Horizontal compression by 1/9: This corresponds to the value of b, which is 1/9.

Moved 11 units up: This corresponds to the value of k, which is 11.

Moved 12 units left: This corresponds to the value of h, which is -12.

Putting it all together, the equation of the logarithmic function is y = -4 * log(base 1/9)(x + 12) + 11.

Answer 2

The equation y = -4log(9(x + 12)) + 11 accurately represents the logarithmic function after all the specified transformations.

Here's the equation of the transformed logarithmic function, along with justifications for each transformation:

Equation: y = -4log(9(x + 12)) + 11

Justifications:

1. Vertical Stretch by 4:

- The coefficient "-4" outside the logarithm function stretches the graph vertically by a factor of 4.

- It makes the graph 4 times taller compared to the original logarithmic function.

2. Reflection in the x-axis:

- The negative sign in front of the logarithm function reflects the graph across the x-axis.

- It flips the graph upside down.

3. Horizontal Compression by 1/9:

- The coefficient "9" inside the logarithm function compresses the graph horizontally by a factor of 1/9.

- It makes the graph 9 times narrower compared to the original function.

- The parentheses around "x + 12" ensure that the compression affects the entire x-expression.

4. Vertical Shift Up 11 Units:

- The constant "11" added to the end of the equation shifts the graph 11 units upward.

- It moves the entire graph vertically upwards.

5. Horizontal Shift Left 12 Units:

- The "-12" inside the parentheses with "x" shifts the graph 12 units to the left.

- It moves the entire graph horizontally to the left.

Complete the question:

Write the equation of a logarithmic function that has been vertically stretched by 4, reflected in the x-axis, horizontally compressed by 1/9, moved 11 units up and 12 units left. Justify your answer.