Function Transformation

What is the effect of adding a constant to a function, such as f(x) + c?

• It shifts the graph of the function vertically; if c is positive, it shifts up, and if c is negative, it shifts down.

• It shifts the graph of the function horizontally; if c is positive, it shifts right, and if c is negative, it shifts left.

• It reflects the graph of the function across the x-axis if c is positive, and across the y-axis if c is negative.

• It stretches the graph of the function vertically if c is positive, and compresses it if c is negative.

What does the transformation f(x + 3) represent?

• The graph of f(x) is shifted to the left by 3 units.

• The graph of f(x) is shifted to the right by 3 units.

• The graph of f(x) is stretched vertically by a factor of 3.

• The graph of f(x) is reflected over the x-axis.

What is the effect of subtracting a constant from the input of a function, such as f(x - c)?

• It shifts the graph of the function vertically; if c is positive, it shifts up, and if c is negative, it shifts down.

• It reflects the graph of the function across the x-axis.

• It shifts the graph of the function horizontally; if c is positive, it shifts right, and if c is negative, it shifts left.

• It stretches the graph of the function horizontally, making it wider or narrower.

What type of function is defined by a linear equation?

• A quadratic function

• A linear function

• An exponential function

• A polynomial function

What is vertical stretch in function transformations?

• Vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

• Vertical stretch occurs when the input values of a function are multiplied by a factor greater than 1, making the graph wider.

• Vertical stretch occurs when the function is reflected over the x-axis, making the graph inverted.

• Vertical stretch occurs when the function is shifted upwards by a constant value.

What is a function transformation?

• A function transformation refers to the changes made to the graph of a function, which can include shifts, stretches, compressions, and reflections.

• A function transformation is the process of finding the derivative of a function.

• A function transformation is a method to integrate a function over a specific interval.

• A function transformation is a technique used to solve differential equations.

What does the transformation h(x) = 1/5f(x) represent?

• The graph of f(x) is vertically compressed by a factor of 5.

• The graph of f(x) is vertically stretched by a factor of 5.

• The graph of f(x) is reflected over the x-axis.

• The graph of f(x) is shifted 5 units to the right.

What does the transformation s(x) = 7f(x) represent?

• The graph of f(x) is vertically stretched by a factor of 7.

• The graph of f(x) is vertically compressed by a factor of 7.

• The graph of f(x) is reflected over the x-axis.

• The graph of f(x) is shifted 7 units to the right.

What does a negative sign in front of a function indicate?

• A reflection of the graph across the x-axis.

• A shift of the graph to the right.

• A stretch of the graph vertically.

• A reflection of the graph across the y-axis.

What is the general form of a quadratic function?

• f(x) = ax^2 + bx + c, where a, b, and c are constants.

• f(x) = ax^3 + bx^2 + c, where a, b, and c are constants.

• f(x) = a + b + c, where a, b, and c are constants.

• f(x) = ax^2 + c, where a and c are constants.