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指数式・指数方程与函数特征进阶

The graph of the equation \( y=4^x+k \) is shown, where k is a constant. What is the value of k?
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指数式・指数方程与函数特征挑战
The functions \( f \) and g are defined by the given equations, where \( x\ge0 \) , a and b are integer constants, \( a<b \) , and \( a>1 \). If \( y=f(x) \) and \( y=g(x) \) are graphed in the xy-plane, which of the following equations displays, as a constant or coefficient, the minimum value of the function it defines, where \( x\ge0 \)?
I. \( f(x)=a(0.54)^{-bx} \)
II. \( g(x)=a(1.46)^{x+2}+b \)
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指数式・指数方程与函数特征挑战

What is an equation of the graph shown?
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指数式・指数方程与函数特征进阶
For the function \( f \), the table shows four values of x and their corresponding values of \( f\left(x\right) \).

Which of the following could describe this function?
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指数式・指数方程与函数特征挑战
What is the y-coordinate of the y-intercept of the graph of \( y=(\frac{3}{11})^{x+1} \) in the xy-plane?
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指数式・指数方程与函数特征挑战
The function h is defined by \( h(x)=a^x+b \), where a and b are positive constants. The graph of \( y=h(x) \) in the xy-plane passes through the points (0, 7) and (2, 22). What is the value of ab?
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指数式・指数方程与函数特征挑战
The function \( f \) is defined by \( f\left(x\right)\ =\ a\left(2.7^x+2.7^b\right) \) , where a and b are integer constants and \( 0<a<b \) . The functions g and h are equivalent to function \( f \), where k and m are constants. Which of the following equations displays the y-coordinate of the y-intercept of the graph of \( y=f(x) \) in the xy-plane as a constant or coefficient?
I. \( g(x)=a(2.7^{x}+k) \)
II.\( h(x)=a(2.7)^x+m \)
I. \( g(x)=a(2.7^{x}+k) \)
II.\( h(x)=a(2.7)^x+m \)
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指数式・指数方程与函数特征进阶

What is an equation of the graph shown?
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指数式・指数方程与函数特征挑战
\( f(x)=4^{-5(x+1)} \)
Which of the following equivalent forms of the given function \( f \) displays, as the base or the coefficient, the y-coordinate of the y-intercept of the graph of \( y=f(x) \) in the xy-plane?
Which of the following equivalent forms of the given function \( f \) displays, as the base or the coefficient, the y-coordinate of the y-intercept of the graph of \( y=f(x) \) in the xy-plane?
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指数式・指数方程与函数特征进阶
For the function \( f \), the table shows four values of x and their corresponding values of \( f(x) \).

Which of the following could describe this function?

Which of the following could describe this function?
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指数式・指数方程与函数特征挑战
The exponential function g is defined by \( g(x)=5·a^{x} \) , where a is a positive constant. If \( g(3)=625 \), what is the value of \( g(5) \)?
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指数式・指数方程与函数特征进阶
Which expression is equivalent to \( x^{20}(x^4) \)?
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