Question 1

Find the intercepts of the absolute value function
-$f(x)=|x+4|-3$
A) $(7,0),(7,0),(0,7)$
B) $(-1,0),(7,0),(0,-1)$
C) $(-1,0),(-7,0),(0,1)$
D) $(1,0),(7,0),(0,1)$

Accepted Answer

To find the x-intercepts, set $f(x) = 0$: $|x+4|-3=0 \Rightarrow |x+4|=3$. This gives $x+4=3$ or $x+4=-3$, leading to $x=-1$ or $x=-7$, so the x-intercepts are $(-1,0)$ and $(-7,0)$. For the y-intercept, set $x=0$: $f(0)=|0+4|-3=1$, so the y-intercept is $(0,1)$.

Question 2

Find the intercepts of the absolute value function
-$f(x)=|x-7|$
A) $(-7,0),(0,-7)$
B) $(-7,0),(0,7)$
C) $(7,0),(0,7)$
D) $(7,0),(0,-7)$

Accepted Answer

The x-intercept occurs when $f(x) = 0$, which happens at $x = 7$, giving us the point $(7,0)$. The y-intercept occurs when $x = 0$, substituting $x = 0$ into $f(x)$ gives $f(0) = |0-7| = 7$, resulting in the point $(0,7)$.

Question 3

Find the intercepts of the absolute value function
-$\mathrm{f}(\mathrm{x})=|\mathrm{x}|-3$
A) $(-3,0),(3,0),(0,3)$
B) $(-3,0),(3,0),(0,-3)$
C) $(-3,0),(0,0),(0,-3)$
D) $(-3,0),(0,-3)$

Accepted Answer

The x-intercepts occur where $f(x) = 0$, so $|x| - 3 = 0$ gives $x = 3$ and $x = -3$. The y-intercept occurs where $x = 0$, so $f(0) = |0| - 3 = -3$. Thus, the intercepts are $(-3,0)$, $(3,0)$, and $(0,-3)$.

Question 4

Find the intercepts of the absolute value function
-$f(x)=|x-1|+4$
A) $(0,1)$
B) $(0,4)$
C) $(0,-3)$
D) $(0,5)$

Accepted Answer

The answer of Find the intercepts of the absolute value...

Question 5

Determine whether the absolute value function $f(x)$ has zero, one, or two $x$-intercepts.
-$f(x)=|x-8|-3$
A) 1
B) 0
C) 2

Accepted Answer

The function $f(x) = |x - 8| - 3$ has two x-intercepts because the absolute value function $|x - 8|$ shifts 8 units to the right and 3 units down, crossing the x-axis at two points.

Question 6

Determine whether the absolute value function $f(x)$ has zero, one, or two $x$-intercepts.
-$f(x)=-|x+9|-21$
A) 1
B) 0
C) 2

Accepted Answer

The absolute value function $f(x) = -|x+9|-21$ is always non-positive because the absolute value $|x+9|$ is always non-negative, and when you negate it and subtract 21, the result is always less than or equal to -21. Therefore, the graph of this function never crosses the x-axis, meaning it has 0 x-intercepts.

Question 7

Determine whether the absolute value function $f(x)$ has zero, one, or two $x$-intercepts.
-$f(x)=-|x+15|$
A) 0
B) 2
C) 1

Accepted Answer

The function $f(x)=-|x+15|$ has one $x$-intercept because the absolute value function $|x+15|$ is always non-negative, and its negation $f(x)$ will be non-positive, touching the $x$-axis only when $x+15=0$, i.e., $x=-15$.

Question 8

Determine the absolute value function $\mathrm{f}(\mathrm{x})$ that has been graphed.
- 
A) $f(x)=|x|+1$
B) $f(x)=|x-1|$
C) $f(x)=|x|-1$
D) $f(x)=|x+1|$

Accepted Answer

The answer of Determine the absolute value function $\mathrm{f}(\mathrm{x})$ that...

Question 9

A) $f(x)=|x|+1$
B) $f(x)=|x-1|$
C) $f(x)=|x+1|$
D) $f(x)=|x|-1$

Accepted Answer

The answer of  
A) $f(x)=|x|+1$
B) $f(x)=|x-1|$
C) $f(x)=|x+1|$
D) $f(x)=|x|-1$...

Question 10

A) $f(x)=|x+3|-6$
B) $f(x)=|x+3|+6$
C) $f(x)=|x-3|+6$
D) $f(x)=|x-3|-6$

Accepted Answer

The answer of  
A) $f(x)=|x+3|-6$
B) $f(x)=|x+3|+6$
C) $f(x)=|x-3|+6$
D) $f(x)=|x-3|-6$...

Question 11

A) $f(x)=|x-3|-2$
B) $f(x)=|x+3|+2$
C) $f(x)=|x+3|-2$
D) $f(x)=|x-3|+2$

Accepted Answer

The answer of  
A) $f(x)=|x-3|-2$
B) $f(x)=|x+3|+2$
C) $f(x)=|x+3|-2$
D) $f(x)=|x-3|+2$...

Question 12

A) $f(x)=-|x+2|+5$
B) $f(x)=-|x-2|-5$
C) $f(x)=-|x+2|-5$
D) $f(x)=|x+2|-5$

Accepted Answer

The answer of  
A) $f(x)=-|x+2|+5$
B) $f(x)=-|x-2|-5$
C) $f(x)=-|x+2|-5$
D) $f(x)=|x+2|-5$...

Question 13

A) $f(x)=-|x-7|+7$
B) $f(x)=-|x+7|+7$
C) $f(x)=-|x+7|-7$
D) $f(x)=|x-7|-7$

Accepted Answer

The answer of  
A) $f(x)=-|x-7|+7$
B) $f(x)=-|x+7|+7$
C) $f(x)=-|x+7|-7$
D) $f(x)=|x-7|-7$...

Quiz 3: Graphing Linear Equations

Find the intercepts of the absolute value function - $f(x) =|x+4|-3$

Find the intercepts of the absolute value function - $f(x) =|x-7|$

Find the intercepts of the absolute value function - $\mathrm{f}(\mathrm{x}) =|\mathrm{x}|-3$

Find the intercepts of the absolute value function - $f(x) =|x-1|+4$

Determine whether the absolute value function $f(x)$ has zero, one, or two $x$ -intercepts. - $f(x) =|x-8|-3$

Determine whether the absolute value function $f(x)$ has zero, one, or two $x$ -intercepts. - $f(x) =-|x+9|-21$

Determine whether the absolute value function $f(x)$ has zero, one, or two $x$ -intercepts. - $f(x) =-|x+15|$

Determine the absolute value function $\mathrm{f}(\mathrm{x})$ that has been graphed. - $Determine the absolute value function \mathrm{f}(\mathrm{x}) that has been graphed. - A) f(x) =|x|+1 B) f(x) =|x-1| C) f(x) =|x|-1 D) f(x) =|x+1|$

Quiz 3: Graphing Linear Equations

Find the intercepts of the absolute value function - f(x) =∣x+4∣−3f(x) =|x+4|-3f(x) =∣x+4∣−3

Find the intercepts of the absolute value function - f(x) =∣x−7∣f(x) =|x-7|f(x) =∣x−7∣

Find the intercepts of the absolute value function - f(x) =∣x∣−3\mathrm{f}(\mathrm{x}) =|\mathrm{x}|-3f(x) =∣x∣−3

Find the intercepts of the absolute value function - f(x) =∣x−1∣+4f(x) =|x-1|+4f(x) =∣x−1∣+4

Determine whether the absolute value function f(x) f(x) f(x) has zero, one, or two xxx -intercepts. - f(x) =∣x−8∣−3f(x) =|x-8|-3f(x) =∣x−8∣−3

Determine whether the absolute value function f(x) f(x) f(x) has zero, one, or two xxx -intercepts. - f(x) =−∣x+9∣−21f(x) =-|x+9|-21f(x) =−∣x+9∣−21

Determine whether the absolute value function f(x) f(x) f(x) has zero, one, or two xxx -intercepts. - f(x) =−∣x+15∣f(x) =-|x+15|f(x) =−∣x+15∣

Determine the absolute value function f(x) \mathrm{f}(\mathrm{x}) f(x) that has been graphed. -