Question

match each exponential function to its graph.
$h(x) = 1.5^x$
$q(x) = 2.5^x$
$m(x) = 3.5^x$
$j(x) = 4.5^x$

Explanation:

Step1: Analyze the base of exponential functions

All functions are of the form \( y = a^x \) where \( a>1 \), so they are increasing exponential functions. The larger the base \( a \), the steeper the graph (faster growth).

Step2: Compare the bases

The bases are \( 1.5, 2.5, 3.5, 4.5 \). So the order of steepness from least to most is \( h(x)=1.5^x \) (least steep), \( q(x)=2.5^x \), \( m(x)=3.5^x \), \( j(x)=4.5^x \) (most steep).

Step3: Match to graphs

• The least steep graph (slowest growth) corresponds to \( h(x) = 1.5^x \) (bottom - right graph, since it rises the slowest).
• The next is \( q(x)=2.5^x \) (top - right graph, steeper than \( h(x) \) but less than the others).
• Then \( m(x)=3.5^x \) (bottom - left graph, steeper than \( q(x) \)).
• The most steep graph (fastest growth) corresponds to \( j(x)=4.5^x \) (top - left graph, rises the fastest).

Answer:

• Top - left graph: \( j(x)=4.5^x \)
• Top - right graph: \( q(x)=2.5^x \)
• Bottom - left graph: \( m(x)=3.5^x \)
• Bottom - right graph: \( h(x)=1.5^x \)