Question 5 \( 0 / 1 \mathrm{pt} \) Determine the parent function from which the graph of the function shown below can be obtained. Next, identify each transformation that can be applied to the parent function in order to obtain the graph of the function shown below. \[ g(x)=|x|-5 \] a) Choose the correct parent function. \( y=x^{2} \) \( y=x^{3} \) \( y=|x| \) \( y=\sqrt{x} \) \( y=\sqrt[3]{x} \) b) Choose the correct transformation (Reflections). \( \square \) Select an answer c) Choose the correct transformation (Stretches/Compressions). Select an answer d) Choose the correct transformation (Vertical Shifts). Select an answer e) Choose the correct transformation (Horizontal Shifts). Select an answer Question Heip: Video Written Example Message instructor Submit Question
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The parent function for \( g(x) = |x| - 5 \) is definitely \( y = |x| \). This absolute value function is the foundation upon which all the transformations are built. In this case, the function has been vertically translated downward by 5 units. So, if you visualize it, the classic V shape of \( y = |x| \) simply drops straight down, making room for that -5 shift! For the transformations: since there are no reflections or stretches/compressions involved in this function, we can simply talk about the vertical shift, which we've identified as moving down 5 units. There are also no horizontal shifts since \( g(x) \) is only altered vertically. So, you've nailed the transformations—it’s like moving your favorite painting down the wall without changing its frame!
