QUESTION IMAGE
Question
question 4 sketch a graph of $f(x)=\begin{cases}-3&\text{if }xleq - 2\\2x + 1&\text{if }-2
Step1: Graph for $x\leq - 2$
The function is $f(x)=-3$ for $x\leq - 2$. It is a horizontal line at $y = - 3$ with a closed - circle at $x=-2$ (since the inequality is $\leq$).
Step2: Graph for $-2
The function is $f(x)=2x + 1$. When $x=-2$, $f(-2)=2\times(-2)+1=-3$. When $x = 1$, $f(1)=2\times1+1=3$. Plot the line segment from the open - circle at $(-2,-3)$ to the closed - circle at $(1,3)$ using the slope - intercept form $y=2x + 1$.
Step3: Graph for $x>1$
The function is $f(x)=1$ for $x>1$. It is a horizontal line at $y = 1$ with an open - circle at $x = 1$ (since the inequality is $>$).
To sketch:
- Draw a horizontal line $y=-3$ starting from $x =-\infty$ up to and including $x=-2$ (put a closed dot at $(-2,-3)$).
- Draw the line $y = 2x+1$ for $x$ values from just greater than $-2$ to $x = 1$. Calculate the $y$ - values for the endpoints: at $x=-2,y=-3$ (open dot as $x>-2$ for this part) and at $x = 1,y=3$ (closed dot as $x\leq1$ for this part).
- Draw a horizontal line $y = 1$ starting from just greater than $x = 1$ (open dot at $(1,1)$) to $x=\infty$.
No specific answer is given in a multiple - choice format as the task is to sketch. If you were to describe the range of the function, we note that the range is $\{-3\}\cup[-3,3]\cup\{1\}=[-3,3]$. But the main task here is the graph sketching as described above.
The function is $f(x)=2x + 1$. When $x=-2$, $f(-2)=2\times(-2)+1=-3$. When $x = 1$, $f(1)=2\times1+1=3$. Plot the line segment from the open - circle at $(-2,-3)$ to the closed - circle at $(1,3)$ using the slope - intercept form $y=2x + 1$.
Step3: Graph for $x>1$
The function is $f(x)=1$ for $x>1$. It is a horizontal line at $y = 1$ with an open - circle at $x = 1$ (since the inequality is $>$).
To sketch:
- Draw a horizontal line $y=-3$ starting from $x =-\infty$ up to and including $x=-2$ (put a closed dot at $(-2,-3)$).
- Draw the line $y = 2x+1$ for $x$ values from just greater than $-2$ to $x = 1$. Calculate the $y$ - values for the endpoints: at $x=-2,y=-3$ (open dot as $x>-2$ for this part) and at $x = 1,y=3$ (closed dot as $x\leq1$ for this part).
- Draw a horizontal line $y = 1$ starting from just greater than $x = 1$ (open dot at $(1,1)$) to $x=\infty$.
No specific answer is given in a multiple - choice format as the task is to sketch. If you were to describe the range of the function, we note that the range is $\{-3\}\cup[-3,3]\cup\{1\}=[-3,3]$. But the main task here is the graph sketching as described above.
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Step1: Graph for $x\leq - 2$
The function is $f(x)=-3$ for $x\leq - 2$. It is a horizontal line at $y = - 3$ with a closed - circle at $x=-2$ (since the inequality is $\leq$).
Step2: Graph for $-2
The function is $f(x)=2x + 1$. When $x=-2$, $f(-2)=2\times(-2)+1=-3$. When $x = 1$, $f(1)=2\times1+1=3$. Plot the line segment from the open - circle at $(-2,-3)$ to the closed - circle at $(1,3)$ using the slope - intercept form $y=2x + 1$.
Step3: Graph for $x>1$
The function is $f(x)=1$ for $x>1$. It is a horizontal line at $y = 1$ with an open - circle at $x = 1$ (since the inequality is $>$).
To sketch:
- Draw a horizontal line $y=-3$ starting from $x =-\infty$ up to and including $x=-2$ (put a closed dot at $(-2,-3)$).
- Draw the line $y = 2x+1$ for $x$ values from just greater than $-2$ to $x = 1$. Calculate the $y$ - values for the endpoints: at $x=-2,y=-3$ (open dot as $x>-2$ for this part) and at $x = 1,y=3$ (closed dot as $x\leq1$ for this part).
- Draw a horizontal line $y = 1$ starting from just greater than $x = 1$ (open dot at $(1,1)$) to $x=\infty$.
No specific answer is given in a multiple - choice format as the task is to sketch. If you were to describe the range of the function, we note that the range is $\{-3\}\cup[-3,3]\cup\{1\}=[-3,3]$. But the main task here is the graph sketching as described above.
The function is $f(x)=2x + 1$. When $x=-2$, $f(-2)=2\times(-2)+1=-3$. When $x = 1$, $f(1)=2\times1+1=3$. Plot the line segment from the open - circle at $(-2,-3)$ to the closed - circle at $(1,3)$ using the slope - intercept form $y=2x + 1$.
Step3: Graph for $x>1$
The function is $f(x)=1$ for $x>1$. It is a horizontal line at $y = 1$ with an open - circle at $x = 1$ (since the inequality is $>$).
To sketch:
- Draw a horizontal line $y=-3$ starting from $x =-\infty$ up to and including $x=-2$ (put a closed dot at $(-2,-3)$).
- Draw the line $y = 2x+1$ for $x$ values from just greater than $-2$ to $x = 1$. Calculate the $y$ - values for the endpoints: at $x=-2,y=-3$ (open dot as $x>-2$ for this part) and at $x = 1,y=3$ (closed dot as $x\leq1$ for this part).
- Draw a horizontal line $y = 1$ starting from just greater than $x = 1$ (open dot at $(1,1)$) to $x=\infty$.
No specific answer is given in a multiple - choice format as the task is to sketch. If you were to describe the range of the function, we note that the range is $\{-3\}\cup[-3,3]\cup\{1\}=[-3,3]$. But the main task here is the graph sketching as described above.