Question

algebra 2a semester online practice
complete this assessment to review what you’ve learned. it will not count toward your grade.
analyze the graphs of $f(x) = |x|$ and $h(x) = |2.3x|$. which statement correctly describes the domain and range changes, if any, from $f(x)$ to $h(x)$? (1 point)

• domain: $mathbb{r}$; range: $y \geq 0$ for both graphs
• domain: $x \geq 0$; range: $mathbb{r}$ for both graphs
• domain: $x \geq 2.3$; range: $y \geq 0$
• domain: $mathbb{r}$; range: $y \geq 2.3$

Explanation:

Step1: Analyze Domain of \( f(x) = |x| \) and \( h(x) = |2.3x| \)

The domain of a function is the set of all possible \( x \)-values. For absolute value functions \( y = |ax + b| \), \( x \) can be any real number (since we can multiply any real number by a constant and take its absolute value). So, the domain of both \( f(x)=|x| \) and \( h(x)=|2.3x| \) is \( \mathbb{R} \) (all real numbers).

Step2: Analyze Range of \( f(x) = |x| \) and \( h(x) = |2.3x| \)

The range of a function is the set of all possible \( y \)-values. For \( f(x)=|x| \), the absolute value of any real number is non - negative, so the range is \( y\geq0 \). For \( h(x)=|2.3x| \), since \( 2.3x \) is a real number (because \( x \) is real and 2.3 is a real constant) and the absolute value of any real number is non - negative, the range is also \( y\geq0 \).

Now let's check the options:

• Option 1: domain: \( \mathbb{R} \); range: \( y\geq0 \) for both graphs. This matches our analysis.
• Option 2: The domain of absolute value functions is not \( x\geq0 \), it's all real numbers, and the range is not \( \mathbb{R} \) (it's non - negative), so this is incorrect.
• Option 3: The domain of \( h(x)=|2.3x| \) is not \( x\geq2.3 \), it's all real numbers, so this is incorrect.
• Option 4: The range of \( h(x)=|2.3x| \) is not \( y\geq2.3 \), it's \( y\geq0 \), so this is incorrect.

Answer:

A. domain: \( \mathbb{R} \); range: \( y\geq0 \) for both graphs