Fill in the blank(s) to correctly complete each sentence. The ...

Question

Fill in the blank(s) to correctly complete each sentence. The graph of ƒ(x) = -(1/3)^x+4-5 is that of ƒ(x) = (1/3)^x reflected across the ______ -axis, translated to the left ______ units and down _______ units.

Accepted Answer

Hello, everyone. We've been asked to complete the sentence by filling in the blanks. The sentence we are given says the graph of F of X equals negative 1/7. Raise to the X minus two power plus 13 is that of F of X equals 1/7. Raise to the X power ref reflected across the blank axis shifted to the right blank units and up blank units. Our answer choices are a why 13 B Y 13 2 C X 2 13 D X 13 2. So thinking about this original function F of X equals negative 1/7 raised the X minus two power plus 13. Looking at this, this reminds me of slope intercept form from what I used to graph at the beginning of algebra. In which case, if this is similar to slope intercept form should be like my Y intercept. So if this is the Y intercept, this means this is saying how much we went up or down from our original base graph. So I'm gonna say that we shifted this 13 units up, so we went up 13 units. The next thing that jumps at me is that I have a negative in front of my 1/7 raise to the X minus two power. I recall that when I had something like a quadratic function and it was a negative, it reflected over the X axis, this will do the same. So our negative up here tells us that this reflects over the X axis. Then our exponent of X minus two tells us how far this will shift left or right. And in this case, we will be shifting this two units to the right. So this will be right two units. So in order filling in the blank, it is reflected across the X axis shifted to the right two units and up 13 units. So we have the blanks X 2 13 and that matches answer choice C have a nice day.

Fill in the blank(s) to correctly complete each sentence. The graph of ƒ(x) = -(1/3)^x+4-5 is that of ƒ(x) = (1/3)^x reflected across the -axis, translated to the left units and down ___ units.

Key Concepts

Reflections of Functions

Horizontal Translations

Vertical Translations

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