y as function of x

Determining if a representation shows y as a function of x.

Relation

x-values do not repeat

Determine if the relation shows y as a function of x.

A)  {(-2, 0.5), (0, 2.5), (4, 6.5), (5, 2.5)}

The x-values, the first number, do not repeat.
This relation does show y as function of x.

Relation

x-values do not repeat

Determine if the relation shows y as a function of x.

B)   {(6, 5), (4, 3), (6, 4), (5, 8)}

The x-value 6 , the first number, DOES repeat.
This relation does NOT show y as function of x.

Multiple Choice

Determine if the relation given shows y as a function of x.

{(6, 2), (7, 2), (16, 1), (8, 2)}  

• Yes, bc none of the x-values repeat

• No, bc the y-value 2 repeat

• Yes, bc y - values do not repeat

• No, bc the x - value 6 repeats

Multiple Choice

Determine if the relation {(9, 5), (4, 3), (10, 4), (9, 8)} shows y as a function of x.

• Yes, bc none of the x-values repeat

• No, bc none of the x-values repeat

• Yes, bc there are two 4s.

• No, bc x value 9 repeats.

Tables

The x-values do not repeat

Determine whether the relation shown on the table shows y as a function of x.

​A.

​B.

​Table B DOES NOT show y as function of x.
The x value 4 repeats twice.

​Table A shows y as function of x.
No x-value is repeating.

Multiple Choice

Determine if the relation given shows y as a function of x.

• Yes, bc none of the x-values repeat

• No, bc none of the x-values repeat

• Yes, bc y - value 0 & 1 repeat

• No, bc y - value 0 & 1 repeat

Mapping

Each input (x-values) has only one output (y-values)

• The input values are in the first oval.

• The output values are in the second oval.

• Only one arrow may leave from each input value.
  

Mapping

Each input (x-values) has only one output (y-values)

​A.

​B.

​Mapping A does show y as a function of x.
Each input value has one output value.

​Mapping B does NOT show y as a function of x.
The input value of 1 has two output values.

Multiple Choice

Determine if the mapping given shows y as a function of x.

• Yes, bc each input has one output

• No, bc the arrows are not in order

• No, bc each input has one output

Multiple Choice

Determine if the mapping given shows y as a function of x.

• Yes, bc each input has one output

• No, bc input 6 has two outputs

• No, bc the output 1 has two inputs

Graphs

Must pass vertical line test

• Draw a vertical line through the graph.

• If the vertical line passes through the graph only one time, then the graph shows y as a function of x.

• If the vertical line passes though multiple spots on the graph, then graph does NOT show y as a function of x.

Graphs

Must pass vertical line test

​Graph A passes the VLT. The line only touches one point.
The graph does show y as function of x.

​Graph B passes the VLT. The line only touches one point.
The graph does show y as function of x.

​Graph C DOES NOT pass the VLT. The line touches twice on the circle.
The graph does NOT show y as function of x.

​A.

​B.

C.

Multiple Choice

Determine if the relation given shows y as a function of x.

• Yes, bc the graph passes the VLT , it only touches once.

• No, bc the graph fails the VLT , it touches twice.

• Yes, bc the graph passes the HLT , it only touches once.

Multiple Choice

Determine if the relation given shows y as a function of x.

• Yes, bc the graph passes the VLT , it only touches once.

• No, bc the graph fails the VLT , it touches twice.

• Yes, bc the graph passes the HLT , it only touches once.

Equations

Must graph equations on caluculator in order to determine

Graphs must pass the vertical line test. The vertical line must only pass through the graph one time.

Equations

Must graph equations on caluculator in order to determine

Equations

Must graph equations on caluculator in order to determine

Equations

Must graph equations on caluculator in order to determine

Multiple Choice

Does the equation $$y\ =\ -3x\ -2$$ , show y as a function of x ?

Hint - graph on desmos. CLICK ON LINK https://www.desmos.com/testing/texas/graphing

• Yes, passes the VLT.

• No, Fails the VLT

• Yes, passes the HLT

Multiple Choice

Does the equation $$x=-2$$ , show y as a function of x ?

Hint - graph on desmos - CLICK ON LINK! https://www.desmos.com/testing/texas/graphing

• Yes, passes the VLT.

• No, Fails the VLT

• Yes, passes the HLT

Domain & Range of relations

Domain:

List of x-values in the relation

​A)  {(-2, 0.5), (0, 2.5), (4, 6.5), (5, 2.5)}

The domain is {-2, 0, 4, 5}

Multiple Choice

What is the domain of  {(6, 11), (4, 3), (8, 4), (5, 9)}

• {4, 5, 6, 8}

• {3, 4, 9, 11}

• {3,4,5,6,8,9, 11}

Range:

List of y-values in the relation

​A)  {(-2, 0.5), (0, 2.5), (4, 6.5), (5, 2.5)}

The range is {0.5, 2.5, 6.5}

Notice 2.5 was only listed 1 time, do not repeat the numbers

Multiple Choice

What is the range of {(6, 11), (4, 3), (8, 4), (5, 9)}

• {4, 5, 6, 8}

• {3, 4, 9, 11}

• {3,4,5,6,8,9, 11}

Multiple Choice

What is the range of the table?

• {2, 3, 4, 5}

• {4, 8, 10}

• {2, 3, 4, 5, 8, 10}

Multiple Choice

What is the domain of the table?

• {2, 3, 4, 5}

• {4, 8, 10}

• {2, 3, 4, 5, 8, 10}

Multiple Choice

What is the domain of the mapping?

• {1, 2, 3, 4}

• {a, b, c, d}

• {1, 2, 3, 4, a, b, c, d}

Multiple Choice

What is the range of the mapping?

• {1, 2, 3, 4}

• {a, b, c, d}

• {1, 2, 3, 4, a, b, c, d}