Function Notation, Graphing Using Slope Intercept and Standard Form, Transformations

Rewrite in slope intercept form.

• y = 3/ 2 x + 8

• y = 3/ 2 x - 8

• y = 2/3 x + 8

• y = 2/3x - 8

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Which could be the graph of the equation y = 1/3x - 2?

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Which graph best represents the equation y = -3x + 4?

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If the graph of the parent function f(x) = x is shifted 7 units
down, which of the following equations would the new graphed
line represent?

• f(x) = 7x

• f(x) = x - 7

• f(x) = x + 7

• f(x) = 7x - 7

What is function notation?

• A way to represent a function using symbols and variables.

• A technique to graph functions on a coordinate plane.

• A way to represent a function using words and phrases.

• A method to solve mathematical equations.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

If f(x) = -4x - 5 and
g(x) = 3 - x,
what is g(-4) + f(1)?

• 7

• -2

• -9

• -10

Answer explanation

To find g(-4), substitute -4 into g(x): g(-4) = 3 - (-4) = 7. For f(1), substitute 1 into f(x): f(1) = -4(1) - 5 = -9. Now, g(-4) + f(1) = 7 - 9 = -2. Thus, the answer is -2.

Tags

CCSS.HSF.IF.A.2

Write the equation in slope-intercept form through (4, -5) and (-4, -1)

• y = -1/2x - 3

• y = 1/2x - 3

• y = -3/2x - 3

• y = 3/2x - 3

Answer explanation

To find the slope (m), use the formula m = (y2 - y1) / (x2 - x1). Here, m = (-1 - (-5)) / (-4 - 4) = 4 / -8 = -1/2. Using point-slope form with (4, -5), we convert to slope-intercept form: y = -1/2x - 3.

Write the equation of the graph.

Answer explanation

The correct equation is \(y=\frac{1}{2}x+3\) because it has a positive slope of \(\frac{1}{2}\) and a y-intercept of 3, indicating the line rises as x increases.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Write an equation in slope intercept form that is perpendicular to y = -3x + 4 and passes through the point (9,5).

• y = 3x - 32

• y = -3x + 22

• y = 1/3x - 8

• y = 1/3x + 2

Answer explanation

The slope of the given line y = -3x + 4 is -3. A perpendicular line has a slope of 1/3. Using the point-slope form with point (9,5), we find the equation y = 1/3x + 2, which matches the correct choice.

Write an equation in slope intercept form that is parallel to y = 2x +3 and passes through the point (3, -4).

• y = 2x + 10

• y = 2x -10

• y = -2x -10

• y= -2x - 2

Answer explanation

To find a parallel line, use the same slope (2) as y = 2x + 3. Using point-slope form with (3, -4): y + 4 = 2(x - 3). Simplifying gives y = 2x - 10, which matches the correct choice.