Junior Cycle Mathematics Functions & Graphs: Draw the graph of the following

Draw the graph of the following function in the domain $-2 \leq x \leq 2$, for $x \in \mathbb{R}$ - Junior Cycle Mathematics - Question 14 - 2018

Question 14

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Draw the graph of the following function in the domain $-2 \leq x \leq 2$, for $x \in \mathbb{R}$. y = 2x + 3 Draw the graph of the following function in the doma... show full transcript

Worked Solution & Example Answer:Draw the graph of the following function in the domain $-2 \leq x \leq 2$, for $x \in \mathbb{R}$ - Junior Cycle Mathematics - Question 14 - 2018

Step 1

Draw the graph of the following function in the domain $-2 \leq x \leq 2$, for $x \in \mathbb{R}$. y = 2x + 3

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Answer

To graph the equation $y = 2x + 3$ , follow these steps:

Identify Key Points: Calculate the y-values at key x-values within the domain.
- For $x = -2$ :
  $y = 2(-2) + 3 = -4 + 3 = -1$
- For $x = -1$ :
  $y = 2(-1) + 3 = -2 + 3 = 1$
- For $x = 0$ :
  $y = 2(0) + 3 = 0 + 3 = 3$
- For $x = 1$ :
  $y = 2(1) + 3 = 2 + 3 = 5$
- For $x = 2$ :
  $y = 2(2) + 3 = 4 + 3 = 7$
The points to plot are:
- (-2, -1)
- (-1, 1)
- (0, 3)
- (1, 5)
- (2, 7)
Plot Points on the Graph: Mark the calculated points on the grid provided.
Draw the Line: Connect the points with a straight line since this is a linear function.
Label the Axes: Ensure the axes are labeled correctly for clarity.

Step 2

Draw the graph of the following function in the domain $-2 \leq x \leq 2$, for $x \in \mathbb{R}$. y = x^2 - 1

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Answer

To graph the equation $y = x^2 - 1$ , follow these steps:

Identify Key Points: Calculate the y-values at key x-values within the domain.
- For $x = -2$ :
  $y = (-2)^2 - 1 = 4 - 1 = 3$
- For $x = -1$ :
  $y = (-1)^2 - 1 = 1 - 1 = 0$
- For $x = 0$ :
  $y = 0^2 - 1 = 0 - 1 = -1$
- For $x = 1$ :
  $y = 1^2 - 1 = 1 - 1 = 0$
- For $x = 2$ :
  $y = 2^2 - 1 = 4 - 1 = 3$
The points to plot are:
- (-2, 3)
- (-1, 0)
- (0, -1)
- (1, 0)
- (2, 3)
Plot Points on the Graph: Mark the calculated points on the grid provided.
Draw the Parabola: Smoothly connect the points to create a U-shaped curve as this is a quadratic function.
Label the Axes: Clearly label both axes for understanding.

Draw the graph of the following function in the domain $-2 \leq x \leq 2$, for $x \in \mathbb{R}$ - Junior Cycle Mathematics - Question 14 - 2018

Worked Solution & Example Answer:Draw the graph of the following function in the domain $-2 \leq x \leq 2$, for $x \in \mathbb{R}$ - Junior Cycle Mathematics - Question 14 - 2018

Draw the graph of the following function in the domain $-2 \leq x \leq 2$, for $x \in \mathbb{R}$. y = 2x + 3

Draw the graph of the following function in the domain $-2 \leq x \leq 2$, for $x \in \mathbb{R}$. y = x^2 - 1

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