Question

describe the transformation. the graph of f is a vertical blank by a factor of blank of the parent blank function. options: stretch, shrink, constant, linear, absolute value, quadratic, \\(\frac{1}{3}\\), 1, 3

Explanation:

Step1: Determine transformation type (stretch/shrink)

Vertical stretch/shrink: If \( y = a f(x) \), \( |a|>1 \) is stretch, \( 0<|a|<1 \) is shrink. Here, factor options: \( \frac{1}{3} \) (shrink), 3 (stretch), 1 (no change). Since we need to pick, let's see parent function. Common parent functions: linear, absolute value, quadratic. Let's assume a parent function (e.g., quadratic \( y = x^2 \), absolute value \( y = |x| \), linear \( y = x \)). For vertical stretch, factor >1; shrink <1. Let's check the blanks. First blank: "stretch" or "shrink". If factor is 3, it's stretch; if \( \frac{1}{3} \), shrink. Let's proceed.

Step2: Choose factor

Options for factor: \( \frac{1}{3} \), 1, 3. Let's see typical transformations. If it's a vertical stretch, factor 3; shrink \( \frac{1}{3} \). Let's assume the parent function (e.g., quadratic, absolute value, linear). Let's pick the most common. Let's say parent function is quadratic (or absolute value, linear). Let's fill the blanks:

First blank: "stretch" (if factor 3) or "shrink" (if \( \frac{1}{3} \)). Let's check the options. Let's suppose the transformation is vertical stretch by factor 3, or shrink by \( \frac{1}{3} \). Let's see the parent function options: linear, absolute value, quadratic.

Let's put it together. Let's say:

The graph of \( f \) is a vertical stretch by a factor of 3 of the parent quadratic (or absolute value, linear) function. Or shrink by \( \frac{1}{3} \). Wait, let's check the options. The parent function options: linear, absolute value, quadratic. Let's pick a common one. Let's assume the parent function is quadratic (or absolute value). Let's take an example: if parent is \( y = x^2 \), and \( f(x) = 3x^2 \), it's vertical stretch by 3. If \( f(x) = \frac{1}{3}x^2 \), shrink by \( \frac{1}{3} \).

Now, the blanks:

1. First blank: stretch or shrink. Let's see the factor. If factor is 3, stretch; if \( \frac{1}{3} \), shrink.

1. Second blank: factor ( \( \frac{1}{3} \), 1, 3 )

1. Third blank: parent function (linear, absolute value, quadratic)

Let's choose the most probable. Let's say vertical stretch by 3, parent quadratic (or absolute value). Let's check the options. Let's proceed:

First blank: stretch (since 3 >1, stretch)

Second blank: 3

Third blank: quadratic (or absolute value, linear). Let's pick quadratic as a common parent function for transformations.

Answer:

The graph of \( f \) is a vertical \(\boldsymbol{\text{stretch}}\) by a factor of \(\boldsymbol{3}\) of the parent \(\boldsymbol{\text{quadratic}}\) function. (Alternatively, if factor is \(\frac{1}{3}\), it's shrink, but 3 is a more common stretch factor. Parent function could also be absolute value or linear, but quadratic is a common one for vertical stretches/shrinks.)