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SSAT Upper Level Math : Geometry

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All SSAT Upper Level Math Resources

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Example Questions

Example Question #474 : Ssat Upper Level Quantitative (Math)

Function

Give the equation graphed in the above figure.

Possible Answers:

y = |x-3| - 5

y = |x+5| - 3

y = |x-5| + 3

y = |x+5| + 3

y = |x+3| + 5

Correct answer:

y = |x+5| + 3

Explanation:

The graph below is the graph of the absolute value function f(x)= |x| , which pairs each -coordinate with its absolute value.

Absolute value graph

The given graph is the above graph shifted right five units and upward three units. The graph of any function y = f(x) shifted right five units and upward three units is y = f(x+5)+3 , so the correct response is y = |x+5| + 3 .

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Example Question #475 : Ssat Upper Level Quantitative (Math)

If the graph of the equation $y= x^{2}+ 3x - 5$ is shifted downward seven units on the coordinate plane, what will be the equation of the resulting graph?

Possible Answers:

$y = x ^{2}+17x+65$

$y= x^{2}+ 3x+2$

$y=\frac{1}{7} x^{2}+ \frac{3}{7}x - \frac{5}{7}$

$y= x^{2}+ 3x - 12$

$y = x ^{2}-11x+23$

Correct answer:

$y= x^{2}+ 3x - 12$

Explanation:

The graph of a function y = f(x) shifted downward seven units is the graph of y = f(x) -7 . In this graph, $f(x)= x^{2}+ 3x - 5$ , so the graph formed by the transformation is that of the equation

$y = ( x^{2}+ 3x - 5)-7$

$y = x^{2}+ 3x -12$

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Example Question #5 : How To Find Transformation For An Analytic Geometry Equation

Function

Give the equation graphed in the above figure.

Possible Answers:

y = |2x|

y = |x-2|

y =|x|-2

y = |x+2|

y =|x|+2

Correct answer:

y = |x-2|

Explanation:

The graph below is the graph of the absolute value function f(x)= |x| , which pairs each -coordinate with its absolute value.

Absolute value graph

The given graph is the above graph shifted right two units. The graph of y = f(x) shifted right two units is y = f(x-2) , so the correct response is y = |x-2| .

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Example Question #1 : Transformation

Function 2

What equation is graphed in the above figure?

Possible Answers:

$y = \left \lceil x\right \rceil - 4$

$y = \left \lfloor x\right \rfloor - 4$

$y = \left \lceil x\right \rceil - 3$

$y = \left \lfloor x\right \rfloor - 3$

$y = \left \lfloor x\right \rfloor +3$

Correct answer:

$y = \left \lfloor x\right \rfloor - 4$

Explanation:

The greatest integer function, or floor function, $y = \left \lfloor x\right \rfloor$ , pairs each value of with the greatest integer less than or equal to . Its graph is below.

Floor function

The given graph is the above graph shifted downward four units. The graph of any function y = f(x) shifted downward four units is y = f(x) - 4 , so the given graph corresponds to equation $y = \left \lfloor x\right \rfloor - 4$ .

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Example Question #201 : Coordinate Geometry

Function 1

What equation is graphed in the above figure?

Possible Answers:

$y = \left \lceil x\right \rceil+ 4$

$y = \left \lfloor x\right \rfloor - 4$

$y = \left \lceil x\right \rceil+ 5$

$y = \left \lfloor x\right \rfloor + 5$

$y = \left \lfloor x\right \rfloor + 4$

Correct answer:

$y = \left \lceil x\right \rceil+ 4$

Explanation:

The least integer function, or celing function, $f(x) = \left \lceil x\right \rceil$ , pairs each value of with the least integer greater than or equal to . Its graph is below.

Ceiling function

The given graph is the above graph shifted upward four units. The graph of any function y = f(x) shifted upward four units is y = f(x) + 4 , so the given graph corresponds to equation $y = \left \lceil x\right \rceil+ 4$ .

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Example Question #12 : Transformation

Function

Give the equation graphed in the above figure.

Possible Answers:

y = |x-5|

y = |x| + 5

y = |x| -5

y = |5x|

y = |x+5|

Correct answer:

y = |x| + 5

Explanation:

The graph below is the graph of the absolute value function f(x)= |x| , which pairs each -coordinate with its absolute value.

Absolute value graph

The given graph is the above graph shifted upward five units. The graph of any function y = f(x) shifted upward five units is y = f(x)+5 , so the correct response is y = |x| + 5 .

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Example Question #251 : Geometry

What is the slope of the line that passes through the points $(-1,4) \text{ and } (-5,1)$ ?

Possible Answers:

$-\frac{3}{4}$

$\frac{4}{3}$

$-\frac{4}{3}$

$\frac{3}{4}$

Correct answer:

$\frac{3}{4}$

Explanation:

Use the following formula to find the slope:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Substituting the values from the points given, we get the following slope:

$\text{Slope}=\frac{1-4}{-5-(-1)}=\frac{-3}{-4}=\frac{3}{4}$

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Example Question #252 : Geometry

Find the slope of a line that passes through the points (17,2) and (-2, -1) .

Possible Answers:

$-\frac{19}{3}$

$\frac{3}{19}$

$\frac{19}{3}$

$-\frac{3}{19}$

Correct answer:

$\frac{3}{19}$

Explanation:

To find the slope of the line that passes through the given points, you can use the slope equation.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{-1-2}{-2-17}=\frac{-3}{-19}=\frac{3}{19}$

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Example Question #253 : Geometry

Find the slope of the line that passes through the points (a, b) and (2, 3) .

Possible Answers:

$\frac{3-b}{2-a}$

$\frac{2-a}{3-b}$

$\frac{2-b}{3-a}$

$\frac{3-a}{2-b}$

Correct answer:

$\frac{3-b}{2-a}$

Explanation:

To find the slope of the line that passes through the given points, you can use the slope equation.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{3-b}{2-a}$

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Example Question #251 : Geometry

A line has the equation 5x-9y=12 . What is the slope of this line?

Possible Answers:

$\frac{9}{5}$

$\frac{5}{9}$

$-\frac{4}{3}$

Correct answer:

$\frac{5}{9}$

Explanation:

You need to put the equation in y=mx+b form before you can easily find out its slope.

5x-9y=12

-9y=-5x+12

$y=\frac{5}{9}x-\frac{4}{3}$

Since $m=\frac{5}{9}$ , that must be the slope.

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Geometry

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #474 : Ssat Upper Level Quantitative (Math)

Example Question #475 : Ssat Upper Level Quantitative (Math)

Example Question #5 : How To Find Transformation For An Analytic Geometry Equation

Example Question #1 : Transformation

Example Question #201 : Coordinate Geometry

Example Question #12 : Transformation

Example Question #251 : Geometry

Example Question #252 : Geometry

Example Question #253 : Geometry

Example Question #251 : Geometry

All SSAT Upper Level Math Resources

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